Test on the discipline theory and structure of the vessel
1. Determine all coefficients of completeness of the ship’s hull, the elements of which:
length (L) – 100 m
width (B) - 14 m
draft (T) - 5.70 m
volumetric displacement of the vessel (V) - 4150 m3
waterline area (S) - 980 m2
midship frame area (?F) - 73 m2
Displacement completeness coefficient (total completeness) ? is the ratio of the volume of the body immersed in water to the volume of a parallelepiped with sides L, B, T.
Waterline area completeness factor? – ratio of the area of the waterline S to the area of a rectangle with sides L, B
The coefficient of completeness of the midship frame area? – ratio of the area of the midship frame to the area of a rectangle with sides B, T
Longitudinal completeness coefficient? – the ratio of the volumetric displacement V to the volume of the prism, the base of which is the area of the midship frame??, and the length is the length of the vessel L.
Vertical fullness ratio? – the ratio of the volumetric displacement V to the volume of the prism, the area of which is the area of the waterline S, and the height of the vessel’s draft T.
2. A ship with a displacement of D = 1600 tons and a center of gravity applica- tion Zg = 4.8 m received a load weighing P1 = 200 t with a center of gravity applica- tion z1 = 3.2 m and then pumped out P2 = 80 tons of ballast with a center of gravity applica- tion z2 = 0.6 m. Determine the new displacement and applicate of the vessel’s center of gravity.
Applying the center of gravity after receiving 200 tons of load:
P1, – cargo weight, t;
z1 – load applicate, m;
Zg – applicate of the vessel’s center of gravity, i.e.
After pumping out 80 tons of ballast, the vessel’s center of gravity is approximated:
P2 – ballast weight, t;
Z2 – applicate of the center of gravity of the evacuated ballast, m;
P – weight displacement of the vessel taking into account the accepted cargo of 200 tons, t;
Z – applicate of the vessel’s center of gravity after accepting a load of 200 t, m.
3. Vessel length L=110 m, width B=12.5 m, draft T=4.20 m, initial transverse metacentric height h=0.75 m, waterline fullness coefficient?=0.81, overall fullness coefficient?=0.77, sea water density? =1.025 t/m3. Determine the change in draft and metacentric height of the vessel, if the vessel has received a load with a mass of P = 40 tons, the center of gravity of which is z = 5.2 m.
To determine the increment of the vessel's draft?T after receiving the cargo, we use the vessel's equilibrium condition, expressed by the equality of the cargo masses P and the additional displacement:
P=?*?V
The volume of the additional layer?V can be considered as the volume of a cylinder, the base of which is the waterline area S, and the height is equal to the change in draft?T
?V=S*?T
Then
P=?*S*?T
The area of the waterline can be found by knowing the fullness coefficient of the waterline and the size of the vessel.
Hence, the change in average draft will be:
Let us determine the weight displacement of the vessel:
D=?*V=?*L*B*T*?=1.025*110*12.5*4.2*0.77=4558 t
? - density of sea water;
L - length of the vessel, m;
B - vessel width, m;
T - vessel draft, m;
? - coefficient of overall completeness.
Change in metacentric height after receiving the load:
P - cargo weight, t;
D is the weight displacement of the vessel, t;
T - draft of the vessel before accepting the cargo, m;
?T - change in vessel draft, m;
h - initial metacentric height, m;
z- applicate of the center of gravity of the accepted load, m.
4. Displacement of the vessel D=3700 t, applicate center of gravity zg=4.7 m. Calculate the new displacement and applicate center of gravity of the vessel if P=100 t of ballast with applicate center of gravity z=0.7 m was rolled overboard.
After pumping out 100 tons of ballast, the vessel’s center of gravity is approximated:
P – ballast weight, t;
Z – applicate of the center of gravity of the evacuated ballast, m;
Zg – applicate of the vessel’s center of gravity, m.
5. On the deck of a passenger ship, n=60 passengers moved to the side at a distance of l=1.8 m from the centerline plane, as a result of which a roll of ?=4° occurred. Determine the value of the initial transverse metacentric height. The mass of one passenger is p=75 kg, the displacement of the ship is D=60 tons.
Weight of all passengers:
P=p*n=75*60=4500kg=4.5t
Heeling moment due to load action:
l – shoulder of passenger movement, m;
P – weight of all passengers, t;
? – roll angle.
Recovery moment:
D – weight displacement of the vessel, t;
? – roll angle;
From the equality of heeling and righting moments:
Since the roll angle is small:
(in radians)
Hence, the value of the metacentric height:
6. Vessel displacement D=500 t, length L=51 m, initial transverse metacentric height h=1.4 m, initial longitudinal metacentric height H=68 m. Calculate the value of the moment that heels the ship by one degree, and the moment that trims by 1m.
The moment that heels the ship by one degree can be determined by the following formula:
D – weight displacement of the vessel, t;
h – value of metacentric height, m.
At small trim angles:
T - difference in draft bow and stern, m;
L is the length of the vessel, m.
Moment that trims the ship by 1 m:
D – weight displacement of the vessel, t;
h – value of metacentric height, m;
L – length of the vessel, m.
7. Displacement of the vessel D=16200 t, applicate of the vessel’s center of gravity zg=8.2 m, applicate of the metacenter zm=9.32 m. Using the table of the shape stability arms (Appendix A), construct diagrams of static and dynamic stability. Using the obtained diagrams, construct a check triangle and determine the maximum dynamic heeling moment that does not lead to capsizing of the vessel?
Initial metacentric height:
h=zm-zg=9.32-8.20=1.12m
Roll angles 0 10 20 30 40 50 60 70
Shoulder shape lк,m 0.000 1.637 3.306 5.051 6.518 7.490 8.032 8.237
sin() 0.000 0.174 0.342 0.500 0.643 0.766 0.866 0.940
Weight arm Zg*sin() , m 0.000 1.424 2.804 4.100 5.270 6.281 7.101 7.705
Stability arm lst 0.000 0.213 0.502 0.951 1.248 1.209 0.931 0.532
Shoulder dynam. ldin,m 0.000 0.019 0.081 0.208 0.400 0.614 0.801 0.928
On the static stability diagram we make auxiliary constructions: draw a tangent from the origin to the stability diagram, draw a vertical line equal to 1 rad = 57.3°. We remove the resulting value of the metacentric height from the diagram, which is equal to h=1.12m
On the dynamic stability diagram we make auxiliary constructions: draw a tangent from the origin to the stability diagram, draw a vertical line equal to 1 rad = 57.3°. We take the value of the overturning moment arm lopr = 0.75 m and the value of the roll angle? = 58°
8. Describe the principle of operation of onboard passive pitching tanks.
The system of on-board tanks with passive impact control is shown in the figure. The large on-board tanks are filled with water, which creates a large moment of resistance to pitching. But water can flow from one tank to another.
In the air channel between the two tanks there is a system of valves, which are activated by a special mechanism depending on the roll of the vessel. Thanks to the pressure difference in the air spaces of the tanks, the flow of liquid and the phase of maximum stabilization of pumping are regulated.
The pitch stabilization system using tanks is designed specifically for each vessel, taking into account model testing. The water level must be strictly defined and adjusted depending on the load of the vessel.
Literature
1. Bronstein D.Ya. Structure and fundamentals of the theory of a vessel - L.: Shipbuilding, 1988.-336 pp.: ill.
2. Malyshev A.N. Buoyancy and stability of fishing vessels.-M.: Mir.2003.-272 p.: ill.
3. Maritime Register of Shipping. Rules for the classification and construction of sea vessels. Volume 1. Eleventh edition. Maritime Register of Shipping. – St. Petersburg, Palace Embankment, 8. 2008. – 502 p.
4. Assessment of landing, stability and strength of the vessel during operation/A.I. Novikov: Textbook - Sevastopol: SevNTU Publishing House, 2003-135 pp.: ill.
5. Samsonov S.V. Elements of buoyancy and stability and their calculation in ship conditions. Vladivostok: Dalrybvtuz, 2001.-60p.
As the density of water changes, the vessel's draft changes. At the same time, with an increase in the density of water, the draft of the vessel decreases and, conversely, with a decrease in the density of the sediment, it increases. The change in vessel draft due to changes in water density can be calculated using the formula:
The amount by which the vessel's draft decreases when moving from fresh water to sea water with a density of 1.025 t/m³ is called fresh water correction , and is usually measured in millimeters. For each ship, this amendment is indicated in the Ship's Load Line Certificate.
The load line, marked on both sides of the ship, shows what minimum freeboard the ship can have in sea water with a density of 1.025 t/m³. When a ship is loading at a port with fresh water, then the load line can be sunk by an amount equal to the fresh water correction. When moving into sea water with a density of 1.025 t/m³, the vessel's draft will decrease by the amount of this amendment, and the vessel will have a load line draft.
When loading in a port where the water density is more than 1,000 t/m³, but less than 1,025 t/m³. The amount by which the load line can be sunk is called the adjustment to the draft for water density (in English, Dock Water Allowance) and can be calculated using the formula:
The draft correction calculated using the above formula is obtained in centimeters.
Example: The vessel's draft at the load line is 6.25 m. The correction for fresh water is 255 mm. The density of water at the berth is 1.009 t/m³. Calculate by what amount the draft can be increased so that with the transition to water with a density of 1.025 t/m³. the vessel had a load line draft.
Calculation order:
1. Calculate how many centimeters the load line can be recessed:
The load line can be recessed by 16 centimeters.
2. Calculate the average draft at which the ship can be loaded:
When determining the weight displacement of a ship based on sediment, if the actual density of the water in which the ship is located differs from the density of the water for which the load scale or hydrostatic curves are calculated, then the correction to the displacement for water density is found using the formula:
It should be noted that as the temperature of water decreases or increases, its density changes. Therefore, if the ship is in fresh water, then it is necessary to take into account its temperature, since when high temperature fresh water its density is below 1,000 t/m³. If this is not taken into account in the calculations, then the difference between the true and calculated displacement can be very significant.
Table of density of fresh water at different temperatures:
| t°C | ρ, t/m³ | t°C | ρ, t/m³ | t°C | ρ, t/m³ |
| 0 | 0,99987 | 12 | 0,99952 | 24 | 0,99732 |
| 1 | 0,99993 | 13 | 0,99940 | 25 | 0,99707 |
| 2 | 0,99997 | 14 | 0,99927 | 26 | 0,99681 |
| 3 | 0,99999 | 15 | 0,99913 | 27 | 0,99654 |
| 4 | 1,00000 | 16 | 0,99897 | 28 | 0,99626 |
| 5 | 0,99999 | 17 | 0,99880 | 29 | 0,99597 |
| 6 | 0,99997 | 18 | 0,99862 | 30 | 0,99537 |
| 7 | 0,99993 | 19 | 0,99843 | 31 | 0,99537 |
| 8 | 0,99988 | 20 | 0,99823 | 32 | 0,99505 |
| 9 | 0,99981 | 21 | 0,99802 | 33 | 0,99472 |
| 10 | 0,99973 | 22 | 0,99780 | 34 | 0,99440 |
| 11 | 0,99963 | 23 | 0,99757 | 35 | 0,99406 |
When the ship is in sea water, the correction for seawater temperature is not taken into account and it is necessary to be guided only by the readings of the hydrometer.
Hydrometer (Densimeter) is a device for measuring the density of a liquid. Modern hydrometers are usually glass. The measurement scale is graduated in kg/m³. The liquid density value is read from the scale division located at the same level as the liquid meniscus, as indicated in Figure 1.
For measurements, use a container with a diameter of at least 50 mm. Sea water samples must be taken from both sides in the midship area from a depth equal to half the vessel's draft, as quickly as possible after removing the draft. 
Rice. 1: Determining the density of water using a hydrometer
It should be noted that the same hydrometer is used to measure the density of water in ballast tanks when determining the amount of cargo based on precipitation. This topic is discussed in detail in the book of the “Marine Practice” series: “Calculation of cargo mass based on drafts.”
Determine the specific cargo capacity and characterize the vessel by purpose and architectural and structural type if:
The cargo capacity of the vessel is W = 181,683 m 3;
The net carrying capacity of the vessel is D h = 144,000 tons.
Solution:
Specific cargo capacity of the vessel:
Vessels with a specific cargo capacity of up to approximately 1.45 m 3 /t are designed for the transportation of heavy and low-volume cargo (bulk and liquid) - according to its intended purpose, this vessel can be a tanker or bulk carrier with a minimum freeboard and one deck.
Task No. 4
How much will the ship's cargo capacity be used or underused if:
Specific loading volume of cargo – u = 1.25 m 3 /t;
Vessel cargo capacity - W c = 22,340 m 3;
The net carrying capacity of the vessel is D h = 14,700 tons.
Solution:
Load volume when full capacity is used:
Underutilized capacity of the ship's cargo spaces:
Problem #5
When loading a ship in two ports, how much cargo can be loaded onto the ship in the second port with the following initial data:
The cargo capacity of the vessel is W c = 63,068 m 3;
Net cargo capacity for this flight - D h = 49,500 tons;
In the first port, cargo was loaded - Q 1 = 20,650 tons;
Specific loading volume of the first cargo - u 1 = 1.5 m 3 /t;
Specific loading of cargo intended for loading in the second port
u 2 = 1.28 m 3 /t.
Solution:
The amount of cargo that needs to be loaded in the second port to fully utilize the vessel's carrying capacity:
Volume occupied by full cargo in the ship's cargo spaces:
Therefore, the full cargo will fit on the ship.
Remaining cargo capacity after loading in the first port:
The amount of cargo that can be accepted at the second port until the ship’s cargo capacity is fully used:
Problem #6
Determine the deadweight of the ship when loading it along the tropical load line if:
The draft of the vessel according to the summer load line is T l = 12.6 m;
The deadweight rating is D W = 54,500 t;
The number of tons that change the draft by 1 cm is a = 59.5 t/cm.
Solution:
Change in vessel draft during the transition from summer to tropical:
Change in the vessel's displacement during the transition from summer to tropical mark:
3. A change in deadweight corresponds to a change in displacement by the same amount:
Task No. 7 Determine the draft of the vessel after receiving the bunker and logistics, if:
The total quantity of accepted reserves is G reserve = 1,060 tons;
The draft of the vessel before receiving supplies is T = 15.26 m;
The number of tons that changes the draft by 1 cm is a = 87.5 t/cm.
Solution:
Change in sediment after receiving supplies:
Vessel draft after receiving supplies:
Problem No. 8
Determine how much cargo a ship can accept in a port with limited depths if:
Deadweight of the vessel - Dw = 22,330 t;
Quantity of voyage reserves - G spare = 580 t;
Draft of the vessel when fully loaded, corresponding to the given navigation area
T c = 9.8 m;
The number of tons that changes the draft by 1 cm - a = 34.8 t/cm;
Restrictions on draft at the loading port - T limit = 9.3 m.
Solution:
Change in vessel draft when loading at a port with limited depths:
The maximum amount of cargo that the ship can accept in accordance with the reserves for the voyage:
Change in vessel loading due to draft restrictions:
The amount of cargo that can be loaded in a port with a draft restriction.