Trim on the bow - the position of the vessel when the draft of the bow is greater than the draft of the stern. Trim on the bow reduces the speed of the vessel
How is the draft and trim of a ship determined?
To determine the draft and trim in the bow and stern, on both sides, marks of depression in decimeters are applied in Arabic numerals. The lower edges of the numbers correspond to the draft they indicate. If the stern draft is greater than the bow draft, then the ship has a trim to the stern and, conversely, if the stern draft is less than the bow draft, the bow is trimmed.
When the bow draft is equal to the stern draft, they say: “the ship is on an even keel”. The mean draft is half the sum of the bow and stern drafts.
What is the displacement and the coefficient of completeness of the vessel?
The main value that characterizes the size of the vessel is the volume of water displaced by it, called volumetric displacement. The same amount of water, expressed in units of mass, is called mass displacement. For the pontoon shown in Fig. 5, the volumetric displacement V will be 10 x 5 x 2 = 100 cubic meters. However, the underwater volume of the vast majority of vessels differs significantly from the volume of a parallelepiped (Fig. 6). As a result, the displacement of the vessel is less than the volume of the parallelepiped built on its main dimensions and draft.
Fig.5
In order to assess the degree of completeness of the underwater surface, the concept of the total completeness coefficient g was introduced into the theory of the vessel, showing what fraction of the volume of the specified parallelepiped is the volumetric displacement of the vessel V. Therefore: V = g x L x B x T
Limits of change of the overall completeness coefficient g
To determine the mass displacement, it is enough to multiply the value of V by the value of the specific mass of water (fresh water - 1000 kg m3, in the World Ocean - from 1023 to 1028 kg m3. The difference between them is called the deadweight, which is the mass of the transported cargo, fuel reserves, lubricating oils, water, provisions, crew and passengers with luggage, i.e. all variable cargo.
Net tonnage is the mass of cargo carried that can be taken on board.
In some cases, such concepts as standard displacement, full, normal and maximum displacement are used.
The standard displacement is the displacement of a completely ready ship, fully manned, equipped with all mechanisms and devices and ready to leave. This displacement includes the mass of SPP equipment ready for action, food and fresh water, excluding fuel, lubricants and boiler water.
The full displacement is equal to the standard dance reserves of fuel, lubricants and boiler water in quantities that provide a given cruising range with full and economical moves.
The normal displacement is equal to the standard displacement, plus the reserves of fuel, lubricants and boiler water in the amount of half the reserves provided for the full displacement.
The largest displacement is equal to the standard plus stocks of fuel, lubricants and boiler water in full in tanks (tanks) specially equipped for this purpose.
After obtaining the value of the average draft MMM, corrections for trim are calculated.
1st correction for trim(correction for displacement of the center of gravity of the current waterline - Longitudinal Center of Flotation (LCF).
1st Trim Correction (tons) = (Trim*LCF*TPC*100)/LBP
Trim - ship trim
LCF - displacement of the center of gravity of the current waterline from the midships
TPC - the number of tons per centimeter of precipitation
LBP - distance between perpendiculars.
The sign of the correction is determined by the rule: the first correction for trim is positive if the LCF and the largest of the forward and aft drafts are on the same side of the midships, which can be illustrated by Table 3.3:
Table 3.3. LCF correction signs
| Trim | LCF nose | LCF feed |
| Stern | - | + |
| Nose | + | - |
Note - it is important to remember the principle: when loading (increasing draft), the LCF always shifts aft.
2nd correction for trim(Nemoto's correction, the sign is always positive). It compensates for the error resulting from the displacement of the LCF position when changing the trim (18).
2nd Trim Correction (tons) =(50*Trim*Trim*(Dm/Dz))/LBP
(Dm/Dz) is the difference in the moment that changes the trim of the ship by 1 cm at two draft values: one 50 cm above the average recorded draft value, the other 50 cm below the registered draft value.
If the ship has hydrostatic tables in the IMPERIAL system, the formulas take the following form:
1st Trim Correction =(Trim*LCF*TPI*12)/LBP
2nd Trim Correction =(6*Trim*Trim*(Dm/Dz))/LBP
Seawater Density Correction
Ship hydrostatic tables are compiled for a certain fixed density of outboard water - on sea vessels, usually at 1.025, on river-sea ships, either at 1.025, or at 1.000, or at both density values simultaneously. It happens that tables are compiled for some intermediate density value - for example, for 1.020. In this case, it becomes necessary to bring the data selected from the tables for calculation into line with the actual density of outboard water. This is done by introducing a correction for the difference between the tabular and actual water densities:
Amendment = Displacement tab *(Density meas - Density tab) / Density tab
It is possible to immediately obtain the displacement value, corrected for the actual seawater density, without correction:
Displacement fact \u003d Displacement table * Density meas / Density table
Displacement calculation
After calculating the values of the average ship draft and trim, the following is performed:
The ship's hydrostatic data determines the ship's displacement corresponding to the average MMM draft. If necessary, linear interpolation is used;
The first and second corrections "for trim" to the displacement are calculated;
The displacement is calculated taking into account corrections for trim, and corrections for the density of outboard water.
The calculation of the displacement, taking into account the first and second corrections for the trim, is carried out according to the formula:
D2 = D1 + ?1 + ?2
D1 - displacement from hydrostatic tables, corresponding to the average draft, t;
1 - first correction for trim (can be positive or negative), t;
2 - second correction for trim (always positive), t;
D2 - displacement, taking into account the first and second corrections for trim, i.e.
The first correction for trim in the metric system is calculated by formula (20):
1 = TRIM × LCF × TPC × 100 / LBP (20)
TRIM - trim, m;
LCF - value of the abscissa of the center of gravity of the waterline area, m;
TPC - the number of tons, by which the displacement changes, with a change in the average draft by 1 cm, t;
1 - First Amendment, vol.
The first correction for trim in the imperial system is calculated by formula (21):
1 = TRIM × LCF × TPI × 12 / LBP (21)
TRIM - trim, ft;
LCF - value of the abscissa of the center of gravity of the waterline area, ft;
TPI - the number of tons by which the displacement changes when the average draft changes by 1 inch, LT / in;
1 - first amendment (may be positive or negative), LT.
The TRIM and LCF values are taken without regard to the sign, modulo.
All calculations in the imperial system are performed in imperial units (inches (in), feet (ft), long tons (LT), etc.). The final results are converted to metric units (MT).
The sign of the correction?1 (positive or negative) is determined depending on the location of the LCF relative to the midships and the position of the trim (bow or stern) in accordance with Table 4.1
Table 4.1 - Signs of correction? 1 depending on the position of the LCF relative to the midships and the direction of the trim
where: T AP - draft at the perpendicular, aft;
T FP - draft at the perpendicular, at the bow;
LCF is the value of the abscissa of the center of gravity of the waterline area.
The second correction in the metric system is calculated by formula (22):
2 = 50 × TRIM 2 × ?MTS / LBP (22)
TRIM - trim, m;
MTS is the difference between MCT 50 cm above the average draft and MCT 50 cm below the average draft, tm/cm;
LBP - distance between the bow and stern perpendiculars of the vessel, m;
The second correction in the imperial system is calculated by formula (23):
2 = 6 × TRIM 2 × ?MTI / LBP (23)
TRIM - trim, ft;
LBP - distance between the ship's fore and aft perpendiculars, ft;
MTI is the difference between MTI 6 inches above mean draft and MTI 6 inches below mean draft, LTm/in;
LBP is the distance between the ship's fore and aft perpendiculars, ft.
All calculations in the imperial system are made in imperial units (inches (in), feet (ft), long tons (LT), etc.). The final results are converted to metric units.
The displacement, taking into account the correction for the density of the outboard water, is calculated by the formula (24):
D = D 2 × g1 / g2 (24)
D 2 - displacement of the vessel, taking into account the first and second corrections for trim, t;
g1 - outboard water density, t/m 3 ;
g2 - tabular density, (for which the displacement D 2 is indicated in hydrostatic tables), t / m3;
D - displacement, taking into account corrections for trim and density of outboard water, m.
13. Sheer the upper deck, which is a smooth rise of the deck from the midships to the bow and stern, also affects the appearance of the vessel. A distinction is made between ships with standard sheer determined by the Load Line Rules, ships with reduced or increased sheer and ships without sheer. Often, sheer is not performed smoothly, but in straight sections with breaks - two or three sections at half the length of the vessel. Due to this, the upper deck does not have a double curvature, which simplifies its manufacture.
The deck line of sea vessels usually has the form of a smooth curve with a rise from the middle part in the direction of the bow and stern and forms a deck sheer. The main purpose of the sheer is to reduce the flooding of the deck when the vessel is sailing in waves and to ensure unsinkability when its extremities are flooded. River and sea vessels with great height freeboard sheer, as a rule, do not have. The rise of the deck in the stern is set, proceeding, first of all, from the condition of non-flooding and unsinkability.
14. Die- this is the slope of the deck from the DP to the sides. Usually, the decks have open decks (upper and superstructure decks). Water falling on the decks, due to the presence of a death, flows down to the sides and from there is discharged overboard. The arrow of death (the maximum elevation of the deck in the DP in relation to the side edge) is usually taken equal to V50 of the width of the vessel. In cross section, the death is a parabola, sometimes, to simplify the manufacturing technology of the hull, it is formed in the form of a broken line. Platforms and decks below the upper deck do not have a camber. The plane of the midship frame divides the ship's hull into two parts - bow and stern. The ends of the hull are made in the form of stems (cast, forged or welded). Nasal
When operating a displacement vessel, it is just as important to monitor the running trim as on a planing vessel.
It is far from always possible to arrange a vessel during design and load it when sailing so that optimal centering and optimal trim are ensured. As you know, excessive running trim leads to a loss of speed, worsens economic performance.
I encountered this problem when I began to test my Duck displacement boat, converted from a small (No. 1) lifeboat(length - 4.5 m; width - 1.85 m). As soon as I gave full throttle to the SM-557L engine, the trim to the stern immediately increased to values clearly exceeding the permissible 5-6 °: wave formation increased, but the speed did not increase.
Began to look for a way to reduce the running trim. By analogy with high-speed boats, I decided to use trim plates. I cut out two transom plates of different shapes with a variable angle of inclination from bakelized plywood and tested them one by one on the Duck. The very first exits showed that at small angles of inclination the plates are ineffective, and at large angles the trim is indeed reduced, but at the same time they begin to work as a brake. When moving on a following wave, strong yaw appears due to the plates; in reverse, the plate blocks the flow of water to the propeller. Whatever it was, but with a capacity of 13.5 liters. with., it was not possible to develop a speed above 10 km / h either with or without plates. The relative speed - the Froude number along the length - fluctuated somewhere around 0.4.
After failing to test the trim tabs, I decided to try installing a specially shaped ring nozzle on the propeller. The nozzle that deflects the jet from the propeller down, according to my calculations, should not only create additional lift on the hull, reducing the running trim, but also at the same time increase the efficiency of the propeller, since the CM-557L engine develops too high a number of revolutions for the possible speed .
The propeller shaft "Duckling" has an inclination relative to the waterline of about 8 °. The front part of the nozzle - from the bow edge to the propeller disk plane - is made coaxially with the propeller shaft. In the plane of the propeller disk, the axial line of the nozzle has a kink - it is inclined downward by 8° (here the angle of inclination to the waterline is already equal to 16°).
As can be seen from the diagram, behind the plane of the screw disk in the upper part of the nozzle, its inner generatrix looks like a straight line. The resulting force P c is decomposed into thrust force and lift force. The stop force was measured with a dynamometer and was equal to 200 kgf. The lifting force P p, which directly reduces the running trim, is approximately equal to 57 kgf.
Now about the manufacture of the nozzle. Trapezoidal slats were cut from foam plastic, which were then glued into a cylinder using epoxy glue. Processing was carried out with a sharp knife and a rasp with a profile check according to templates. Outside, the finished nozzle was pasted over with two layers of fiberglass on epoxy glue. The inner surface of the nozzle is coated with epoxy putty, into which flake graphite is rubbed to reduce friction.
Two aluminum squares are fixed at the top and bottom, tightened with M6 bolts. These bolts and round slings made of Ø 2 mm steel cable securely fasten the nozzle and angles into one piece. The front ends of the squares are attached to the sternpost, the rear ends to the rudder post (ruder post).
The ends of the propeller blades are cut along the inner diameter of the nozzle with an annular gap of 2-3 mm.
With the “Duckling” nozzle, I have already successfully completed two navigations. During this period, the following has been established:
- speed increased from 10 to 12 km/h (Froude number approx. 0.5);
- running trim is practically absent;
- even on a steep following wave, the boat obeys the helm well, and the propeller is almost not exposed;
- the boat moves reliably and satisfactorily obeys the helm in reverse.
Installing an outboard motor on any water-mixing boat, be it a fofan, a dinghy or a four-oared yawl, always causes a strong trim to the stern, which increases with increasing speed. In an article about the Pella boat, it was noted that its speed under the Veterok motor (8 hp) is 9.16 km / h when the driver is sitting on the stern bank, and 11.2 km / h when he sits on the nose. Here is a clear indicator of how running trim affects speed. But there are other disadvantages of such a landing. It is enough to mentally draw a straight line from the eyes of the helmsman, sitting on the stern, forward through the upper point of the stem to make sure that objects on the water in front are not visible to him. With such a poor view of the course, the operation of any vessel is prohibited. Two exits can be suggested; put ballast in the bow of the boat or install a nozzle on the propeller.
If factories producing outboard motors master the production of profiled anti-trim nozzles, a lot of gasoline will be saved, and most importantly, the operating conditions of boats will improve, navigation safety will increase; in any case, the risk of collision with floating obstacles will decrease.
INTRODUCTION 2
1. THE CONCEPT OF THE LONGITUDINAL STABILITY OF THE SHIP.. 3
2. SHIP TRIM AND TRIM ANGLE.. 6
CONCLUSION. nine
REFERENCES.. 10
INTRODUCTION
Stability - the ability of a floating facility to withstand external forces that cause it to roll or trim and return to a state of equilibrium after the impact of external forces (External impact may be due to a wave blow, a gust of wind, a change in course, etc.). This is one of the most important seaworthiness qualities of a floating craft.
The stability margin is the degree of protection of a floating craft from capsizing.
Depending on the plane of inclination, there are transverse stability with roll and longitudinal stability with trim. With regard to surface vessels, due to the elongation of the shape of the ship's hull, its longitudinal stability is much higher than the transverse one, therefore, for the safety of navigation, it is most important to ensure proper transverse stability.
Depending on the magnitude of inclination, stability at small angles of inclination (initial stability) and stability at large angles of inclination are distinguished.
Depending on the nature of the acting forces, static and dynamic stability are distinguished.
Static stability - considered under the action of static forces, that is, the applied force does not change in magnitude.
Dynamic stability - considered under the action of changing (that is, dynamic) forces, such as wind, sea waves, cargo movement, etc.
The most important factors affecting stability are the location of the center of gravity and the center of gravity of the vessel (CV).
1. THE CONCEPT OF THE LONGITUDINAL STABILITY OF THE SHIP
Stability, which manifests itself with the longitudinal inclinations of the vessel, i.e., with trim, is called longitudinal.
Despite the fact that the trim angles of the vessel rarely reach 10 degrees, and usually make up 2-3 degrees, the longitudinal inclination leads to significant linear trims with a large length of the vessel. So, for a ship with a length of 150 m, the angle of inclination is 1 deg. corresponds to a linear trim equal to 2.67 m. In this regard, in the practice of operating ships, issues related to trim are more important than issues of longitudinal stability, since for vehicles with normal ratios of the main dimensions, longitudinal stability is always positive.
With the longitudinal inclination of the ship at an angle ψ around the transverse axis, the C.V. will move from point C to point C1 and the support force, the direction of which is normal to the current waterline, will act at an angle ψ to the original direction. The lines of action of the original and new direction of the support forces intersect at a point.
The point of intersection of the line of action of the support forces at an infinitesimal inclination in the longitudinal plane is called longitudinal metacenter M.
The radius of curvature of the displacement curve of the C.V. in the longitudinal plane is called longitudinal metacentric radius R, which is determined by the distance from the longitudinal metacenter to the C.V.
The formula for calculating the longitudinal metacentric radius R is similar to the transverse metacentric radius;
where IF is the moment of inertia of the waterline area relative to the transverse axis passing through its C. T. (point F); V - volumetric displacement of the vessel.
The longitudinal moment of inertia of the waterline area IF is much greater than the transverse moment of inertia IX. Therefore, the longitudinal metacentric radius R is always much larger than the transverse r. It is tentatively considered that the longitudinal metacentric radius R is approximately equal to the length of the vessel.
The basic position of stability is that the restoring moment is the moment of the pair formed by the ship's weight force and the supporting force. As can be seen from the figure, as a result of the application of an external moment acting in the DP, called trimming moment Mdif, the ship has received a small trim angle ψ. Simultaneously with the appearance of the trim angle, a restoring moment Mψ arises, acting in the opposite direction to the action of the trim moment.
The longitudinal inclination of the ship will continue until the algebraic sum of both moments becomes equal to zero. Since both moments act in opposite directions, the equilibrium condition can be written as an equality:
Mdif = Mψ.
The restoring moment in this case will be:
Мψ = D" × GK1 (1)
where GK1 is the shoulder of this moment, called shoulder of longitudinal stability.
From a right triangle G M K1 we get:
GK1 = MG × sinψ = H × sinψ (2)
The value MG = H included in the last expression determines the elevation of the longitudinal metacenter above the C.T. of the vessel and is called longitudinal metacentric height.
Substituting expression (2) into formula (1), we obtain:
Мψ = D" × H × sinψ (3)
where the product D "× H is the coefficient of longitudinal stability. Keeping in mind that the longitudinal metacentric height H \u003d R - a, formula (3) can be written as:
Мψ \u003d D "× (R - a) × sinψ (4)
where a is the elevation of the C. T. of the vessel above its C. V.
Formulas (3), (4) are metacentric formulas for longitudinal stability.
Due to the smallness of the trim angle in these formulas, instead of sin ψ, you can substitute the angle ψ (in radians) and then:
Mψ = D" × H × ψ or Mψ = D" × (R - a) × ψ.
Since the value of the longitudinal metacentric radius R is many times greater than the transverse r, the longitudinal metacentric height H of any vessel is many times greater than the transverse one h. therefore, if the ship has lateral stability, then the longitudinal stability is assured.
2. SHIP TRIM AND TRIM ANGLE
In the practice of calculating the inclinations of the vessel in the longitudinal plane, associated with the determination of the trim, instead of the angular trim, it is customary to use a linear trim, the value of which is determined as the difference between the draft of the vessel bow and stern, i.e. d = TN - TC.
The trim is considered to be positive if the ship's draft is greater with the bow than with the stern; stern trim is considered negative. In most cases, ships sail with a trim to the stern.
Let us assume that a vessel floating on an even keel along the waterline VL, under the influence of a certain moment, received a trim and its new effective waterline took position V1L1. From the formula for the restoring moment, we have:
ψ \u003d Mψ / (D "× H).
Let's draw a dotted line AB, parallel to VL, through the point of intersection of the aft perpendicular with V1L1. Trim d - is determined by the leg BE of the triangle ABE. From here:
tg ψ ≈ ψ = d / L
Comparing the last two expressions, we get:
d / L = Mψ / (D" × H), hence Mψ = (d / L) × D" × H.
Consider methods for determining the ship's draft under the action of a trimming moment on it, which occurs as a result of the movement of cargo in the longitudinal-horizontal direction.
Let us assume that the load p is moved along the ship by a distance lx. The movement of cargo, as already indicated, can be replaced by the application of a moment of a pair of forces to the ship. In our case this moment will be trimming and equal to:
P × lx × cosψ = D" × H × sinψ
whence tgψ = (P × lx) / (D" × H)
Since small ship inclinations occur around an axis passing through the C. T. F of the waterline area, the following expressions can be obtained for the change in draft fore and aft:
Consequently, drafts fore and aft when moving cargo along the ship will be:
Considering that tgψ = d/L and that D" × H × sinψ = Mψ, we can write:
where T is the ship's draft when positioned on an even keel;
M1cm - the moment that trims the ship by 1 cm.
The value of the abscissa XF is found from the "curves of the elements of the theoretical drawing", and it is necessary to strictly take into account the sign in front of XF: when the point F is located forward of the midship, the value of XF is considered positive, and when the point F is located aft of the midship - negative.
The arm lx is also considered positive if the cargo is carried towards the bow of the ship; when transferring cargo to the stern, the shoulder lx is considered negative.
CONCLUSION
Stability is one of the most important seaworthiness qualities of a floating craft. With regard to ships, a clarifying characteristic of the ship's stability is used. The stability margin is the degree of protection of a floating craft from capsizing.
External impact can be caused by a wave impact, a gust of wind, a change in course, etc.
In the practice of calculating the inclinations of the vessel in the longitudinal plane, associated with the determination of the trim, instead of the angular trim, it is customary to use a linear trim.
BIBLIOGRAPHY
1. I., A., S. Control over the landing, stability and stresses of the ship's hull: Proc. allowance - Vladivostok, Moscow State University. adm. G. I. Nevelskoy, 2003. - 136 p.
2. N. Operational calculations of the seaworthiness of the vessel - M .: Transport, 1990, 142s.
3. K., S. The general arrangement of courts. - Leningrad: "Shipbuilding". - 1987. - 160s.
4. D. Theory and arrangement of the vessel. - Textbook for river schools and technical schools. M.: Transport, 1992. - 248s.
5. D. Device of the vessel: Textbook. - 5th ed., stereotype: - L.: Shipbuilding, 1989. - 344 p.