£39.£G6l|:r 73> A UNITED STATES DEPARTMENT OF COMMERCE PUBLICATION +%«* «*€) i**: l\ ¥\ *^«i o» ' TRIM AND STABILITY GUIDE Container and Barge Carrying Ships U.S. DEPARTMENT OF COMMERCE Maritime Administration TRIM AND STABILITY GUIDE For Container and Barge Carrying Ships U.S. DEPARTMENT OF COMMERCE Peter G. Peterson, Secretary James T. Lynn Under Secretary Maritime Administration Robert J. Blackwell, Assistant Secretary for Maritime Affairs Q. O J a «> a ■6 JULY 1972 For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C, 20402— Price $1.00 Digitized by the Internet Archive in 2012 with funding from LYRASIS Members and Sloan Foundation http://archive.org/details/trimstabilityguiOOwals FOREWORD The introduction of new modes and concepts in transporting waterborne commerce, such as roll-on/roll-off, container and barge carrying ships, has created the need for additional training of merchant marine personnel. In order to maintain the level of competence demanded by these complex and sophisticated ship designs, a high degree of technical knowledge will be mandatory. Among these technical requirements, the capability of maintain- ing ships' stability is of major importance. In preparing this Guide, the author has undertaken the task of putting into seafarer's language the proper use of the ship's Trim and Stability Book and the function and methods used in computing the mathematical formulas required in determining trim and stability, longitudinal strength, forces generated by rolling and pitching, and use of anti-roll tanks. The Guide is not intended to replace the ship's Trim and Stability Book. This publication has been prepared as an instructional guide by the Maritime Administration in its continuing effort to assist the maritime industry in advancing the technological aspects of ship operation in terms of safety, efficiency and economics. HJlA4~ M. L2&IC £> CcU(^ \ „ ROBERT J. BLACKWELL Assistant Secretary for Maritime Affairs in ACKNOWLEDGEMENT This "Guide" has been prepared for the Merchant Marine deck officer serving on the efficient and complicated container and barge carrying ships. It is intended to improve his ability to safely operate these complex vessels by providing a fresh look at the following subjects: a. trim and stability b. longitudinal strength c. anti roll tanks d. forces generated by rolling and pitching e. use of the Trim and Stability book This publication was written by W. Michael Walsh, Naval Architect and Master Mariner, from the Office of Ship Construction, Maritime Administration. The project was initiated and managed by Howard Patteson of the Office of Maritime Manpower, Maritime Administration. The preliminary review was rendered by Ronald K. Kiss, and guidance and advice was tendered throughout by L. Franklin Robertson, both Supervisory Naval Architects, Office of Ship Construction, Maritime Administration. The project was sponsored by Arthur W. Friedberg, Chief, Office of Maritime Manpower, Maritime Administration. The Maritime Administration acknowledges with sincere appreciation the assistance of the following qualified authorities from other organizations whose review and critique contributed substantially to the publication: Professor Norman A. Hamlin, Webb Institute William H. Garzke, Naval Architect, G.G. Sharp, Inc. Captain M. B. Lemly, M.M.T., U.S.C.G. Captain J. N. Caffrey, M.V.P., U.S.C.G. Cdr. R. C. Hill, M.M.T., U.S.C.G. Lt. Cdr. D. L. Folsom, R&D, U.S.C.G. Captain S.F. Sammis, Chief Surveyor, National Cargo Bureau Professor A.R. Philbrick, Texas Maritime Academy Asst. Professor R. W. Armstrong, Texas Maritime Academy Lt. Cdr. Joseph F. Nichols, Maine Maritime Academy J. M. Alanko, Asst. Chief of Construction, U.S. Lines R. O. Patteson, Master Mariner, Consultant to U.S. Lines In addition this book would not have been possible without the skillful efforts of the drafting section, secretarial personnel, and Mr. L. Johnson of the Office of Ship Construction, Maritime Administration. CONTENTS PAGE FOREWORD iii ACKNOWLEDGEMENT v PART I - A STABILITY AVAILABLE Section A-l Review of Math 1 Familiarity w/Trim & Stability Book 5 Quiz 5 Section A- 2 Calculation of KG 6 Calculation of Transverse Metacenter KMt 9 Calculation of GMt 12 Fundamentals of Transverse Stability 13 Section A-3 Stability at Large Angles of Heel — Righting Arms 17 - Curves of Statical Stability 18 — Cross Curves of Stability 21 - Form Gain 21 Section A-4 Free Surface 23 Section A-5 Rolling Period 26 Section A-6 Pitching 29 Section A-7 Trim 30 Section A-8 Ballasting 32 PART I-B SUBDIVISION Section B-9 Floodable Length 36 PART I-C SHIP OPERATION Section C-10 Anti Roll Tanks 39 Section C-l 1 Container Ship Operation 42 Section C-l 2 Barge Carrying Ship Operation 51 Section C-l 3 Damaged Stability 54 PART II TRIM & STABILITY BOOK Section - 14 Instructions & Routine Operating Instructions 66 Section - 1 5 Tank Capacity & Free Surface Table 68 Section - 1 6 Gain in GMt By Ballasting Table 69 vu PAGE Section - 17 Section - 18 Section - 1 9 Section - 20 Section - 21 Section - 22 Section — 23 Trim Table ll Hydrostatics Table ,s Container Stowage Table-Calculation 'J> Lighter Stowage Table 76 Trim & Stability Sheet - (Long Form) • • '° Longitudinal Strength °* Short Form (z-Nomogram) PART III PROBLEM SOLUTION Section - 24 Mechanical & Electronic Stability & Longitudinal Strength Calculators Section - 25 Problems of Ship Operation 95 97 vni STABILITY AVAILABLE PART l-A-1 REVIEW OF MATH Review of Math Because stability is dependent on the position of the vertical center of gravity, it is important to be able to locate the center of gravity by means of calculations. The center of gravity or centroid is a point and it may be calculated for an area, volume or weight. The center of gravity of a system of weights is that point at which we may regard the whole system as being concentrated. The center of gravity is located vertically, longitudinally, and transversely. The calculation of the Center of gravity is determined by the principle of moments. What is a moment? It is a weight multiplied by a distance or an area or volume multiplied by a distance. Distance is measured from center of gravity or centroid of the weight, volume or space to axis that moment will be taken about. - As an example: 2 TON WEIGHT + in 1 Moment of W about AA' is = 2 tons x 5' = 1 ft. tons .A- FIGURE 1 2.5* D in C 5.0' in 2.5**" III L I II <=> o I CO in A B 10.0' FIGURE 2 What is the moment of area BCDE about AA'? Break up figure into 3 increments called I, II, III. The CG of I will be 2.5' above AA'. The CG of II will be 5.75' above AA'. The CG of III will be 6.5' above AA'. Space Area Lever Moment I 5x 10 = 50 ft. 2 x 2.5' = 125.0 ft. 3 II 2.5 x 1 .5 = 3.75 ft. 2 x 5.75' = 21.5 ft. 3 III 2.5 x 3.0 = 7.5 ft. 2 x6.5' = 48.7 ft. 3 61.25 ft. 2 195.2 ft. 3 Moment is 195.2 ft. 3 Area is 61.25 ft. 2 To find height of CG about AA' divide area into moment 195.2 ft. 3 =3.18' above AA' 61.25 ft. 2 The center of gravity of a system of weights is that point at which we may regard the whole system as being concentrated. The center of a space in a liquid such as the center of the volume displaced by a ship's hull is the point at which we may assume the whole upward buoyant force as being concentrated. The deck officer must be familiar with math to perform the following: Calculation of GM Calculation of KM Calculation of KG Calculation of Free Surface Calculation of Trim Understanding of Damage Stability Ability to read and apply Curves of Form, Cross Curves of Stability & Floodable Length Curves Calculation of Stability by use of Long Form Calculation of Stability by use of Short Form Calculation of Stability by Stabiloguage Theory of Moments Simply, almost all stability calculations invojve the theory of moments. Basically the moment is an area, volume or weight multiplied by a distance about an axis. The distance is measured from the center of gravity of the area, volume, or weight to the axis. The moment may be measured as ft tons i.e. weight x distance, ft 4 i.e. volume x distance, ft 3 i.e. area x distance. TABLE OF CENTROIDS (CG) A B/2 COMMON GEOMETRIC SHAPES FIGURE 3 + RECTANGLE t A/2 — 1» ♦ RIGHT TRIANGLE TRIANGLE C.G.® INTERSECTION OF MEDIANS PARALLELOGRAM C.G. IS @ INTERSECTION OF THE DIAGONALS _ 2 r s CIRCULAR SECTOR C . G ^-jf- ABOUT X-x axis QUARTER CIRCLE C.G.=.424r SEMI CIRCLE C.G. ABOUT x = ABOUT y=44 or *24r 3tt PROBLEMS How far is cent r o i d (CG) above base A-A' Determine the coordinates of the centroid of the area with respect to x & y axes A hole having an area of 10" 2 is cut out of the plate whose dimensions are shown in the figure at left. Locate the centroid of the remaining area with respect to the given axes. Locate the centroid of the shaded area with respect to the x & y axes Find the coordinates of the shaded area with respect to the x & y ixes. FAMILIARITY W/TRIM & STABILITY BOOK The Trim and Stability Book is prepared by the contractor for the use of the ship's personnel. The book has been prepared to enable operating personel to determine the vessel's operating metacentric height (corrected GM for any condition of loading or operation). The book will be tailored to the ship, the trade that it will be in, and the cargoes it will carry. In general the contents of the book will be as follows: 1 . The books will show loading conditions that will represent any cargo loading having tonnages and vertical centers of gravity similar to those shown. 2. The book will contain instructions for operation. Including instructions for computation of vessels stability & trim (long form and short form). 3. Routine operating instructions regarding ballasting, tankage and cross connections will also be shown. 4. Instructions for carriage of grain and bulk cargoes and free surface corrections. 5. A table of hydrostatics vs. draft. 6. Trimming table showing profile of ship and containing a trim problem worked out. 7. Table of "Gain in GM by ballasting" shown on a tank vs. displacement basis. 8. "Composite curve of GM required" laid out for GMt required in feet vs. draft. 9. Tank capacity and free surface table. Including VCG, LCG & F/S for slack & 98%-5° heel conditions. 10. Cargo space capacity table including name of space, location, capacity in grain, bale, VCG, & LCG. 11. Long form loading conditions showing mean draft, VCG, LCG, KM, GMt, F/S correction, GMt corrected, trim, trimming lever, LCF location, & drafts at marks. 1 2. Most books contain a short form with an example calculated. A-1 QUIZ 1 . If a ship has a pair of large wing tanks that were empty should the cross connections be left open or closed? 2. When leaving port how would the GMt required be determined? 3. What is the trim lever? 4. What is the USCG's standard of GMt required based on? 5. What is the Maritime Administration's standard of GMt required based on? 6. How is the light ship KG of a ship determined? 7. A vessel floating at her light draft displaces 10,000 tons with a VCG of 28.00'. She loads 12,000 tons of cargo at a VCG of 44.00', 123 tons of F.W at a VCG of 12.4'. 10 tons of lube oil at a VCG of 7.2'. 25 tons of provisions at a VCG of 40.0'. What is her new VCG? 8. If the KMt in the loaded condition for the ship in problem 7 is 33.70' and the free surface correction is 1 5,1 1 9 ft. 4 what is the GMt available? 9. If the trimming moment of a ship is 109,750 ft. tons by the stern and the MT1' is 3,155 ft. tons what is the trim in feet? 10. If a ship of 27,000 tons displacement with a VCG of 3 1 .41 ! loads 336 tons of F.O in a D.B with a VCG of 2.7' what is the GMt available? 1 1 . What axis does the ship trim about? A-2 CALCULATION OF KG & LCG Before stability calculations can be made the light displacement KG must be known. This was determined by the inclining experiment. The KG of any ship is continually changing. It may change quite quickly during operations involving loading and discharging of cargo, bunkering, and storing. At sea the KG generally changes (slowly) due to consumption of liquids, stores and ballasting. The KG might also be affected by icing, and free surface. As cargo operations begin, every weight that is added or removed will affect the displacement and original center of gravity. In order to find the new KG the theory of moments must be applied. The position of the centers of gravity of cargo, fuel, water and stores must be estimated. Multiply each weight by the height of it's CG above the keel to obtain the vertical moment. The sum of all vertical moments is the total vertical moment. The sum of all weights is the total weight. Divide total weight into total vertical moment to obtain new VCG. (You must include the light ship weight and the moment from light ship weight x light ship KG). KG = total vertical moment total weights Example: If we load a barge weighing 700 tons that has a VCG of 5' with 200 tons of sand at a VCG of 2.5' what is the new VCG of the barge? 2.5 •-[ FIGURE k barge sand total W 700 tons x 200 tons x VCG vertical moment 5.0' = 3500 ft. tons 2.5' = 500 ft. tons 900 tons 4.43' 4000 ft. tons Example: If #4 hold was loaded as follows determine the VCG. TILE 50 TONS I R&LFS OF PAPER 50 TONS MACH'Y 100 TONS PIPE 150 TONS -+ STEEL PLATING 300 TONS DOUBLE BOTTOM in ] ^ CD ' 1 i m 10 ' \ FIGURE 5 Item Wgt VCG Moment Stl. PI. 300 7.5 2250 Machy 100 12.5 1250 Pipe 150 15.0 2250 Paper 50 17.5 875 Tile 50 22.5 1125 650 11.92 7750 FIGURE 6 Example 450'- 0" 250'- 0" ^ffOO/TON^ 350'- 0' If a 1 0,000 ton ship with a VCG of 20' is loaded in holds 1 , 2, 3 and 4 as shown what is the VCG of ship in the loaded condition? W VCG Vertical Moment ship 10,000 ton X 20' = 200,000 ft. tons hold#l 750 " X 12.5' 9,350 " t'f " #2 500 " X 10.0' 5,000 " •>•> " #3 1,000 " X 19.0' = 19,000 " •>•> " #4 600 " X 11.0' 6,600 " •>•> 12,850 tons 18.6' 239,950 ft. tons Example: What is the longitudinal center of gravity i.e. what is the longitudinal location of the center of gravity, (take moments about F. P.) W lever long'l moment ship 10,000 tons 250' 2,500,000 ft. tons hold #1 750 tons 100' 75,000 " " " #2 500 " 200' 100,000" " " #3 1,000 " 350' 350,000 " " " #4 600 " 450' 270,000 " " 12,850 tons 256.5 'aft of F.P 3,295,000 ft. tons Problems 1 . Attwood and Pengelly "Theoretical Naval Architecture" page 74 problem 1 . 2. Define Center of Gravity 8 3. La Dage and Van Demert - Stability and Trim for the Ship's Officer page 29 problem 2 page 29 problem 3 page 29 problem 4 CALCULATION OF THE TRANSVERSE METACENTER KMt What is KMt? If the ship is inclined a small amount up to about 7° or sometimes 10° then a vertical line passing through the new Center of Buoyancy will intersect the original vertical line at M. This M is the locus of the Center of Buoyancy or the point about which it rotates. The distance M above the keel is KMt. Another way of saying it is to say KMt = KB + BMt. An approximate way of calculating KB (height of center of bouyancy above keel) is to use Morrish's formula KB= l/3(5T/2 - V/A) where T is draft in feet V is volume of disp. in ft. 3 A is waterplane area in ft. 2 A simpler way of determining KB is to use the curves of form or table of hydrostatic properties in the T&S book. BMt is the vertical distance from B to Mt. It can be calculated by the following formula where I = moment of inertia of waterplane about C.L. also known as the second moment of area, in ft. 4 V = volume of displacement in ft. 3 For a rectangular waterplane the formula is as follows: I = L x B 3 12 where L = length of waterplane B = breadth of waterplane To find the moment of inertia of waterplanes other than rectangular: I = LxB 3 xk where k is a constant depending upon the value of the waterplanes coefficient as follows: Waterplane coef. k Average .70 .042 .75 .048 .80 .055 .85 .062 Example: Calculate the KM for a rectangular barge that has the following characteristics length = 80' beam = 30' draft = 1 0' lb 3 = 80 x 30 3 „ , I = = 180,000 ft. 4 V= 1 xbxd = 80'x 30' x 10' = 24,000 ft 3 12 12 BM =I/V= 180,000 = 7.50' 24,000 because it is a rectangular barge KB = draft = 10=5.00! 2 2 KM = BM + KB = 7.50' x 5.00'= 12.50' Example: Let us increase the beam of the barge by 1 5' and see what happens: I = 80 x 45 3 = 80 x 91 ,1 25 = 607,500 ft. 4 12 12 V = 80x45 x 10= 36,000 ft. 3 BM = I/V = 607,500= 16.88' 36,000 KB = 5.00' KM = BM + KB = 16.88' + 5.00' = 21.88' 10 As a result of the increase of the beam by 50% we have increased the BM by 225% and the KM by 175%. Example: A 68c class container ship is floating at a draft of 29' the displacement is 28,861 tons, the characteristics are as follows: length on waterplane 670' beam 85' tons per inch immersion 96.7' Calculate the KMt and check against the hydrostatic properties in T&S book. waterplane coeff. = 96.7x420 = .713 670x85 waterplane coeff. of .71 3, K = .044 I = 670 x 85 3 x .044 = 18,104,405 ft. 4 V= = 28,861 tons x 35 = 1,010,135 ft. 3 BM = I/V= 18,104,405 ft. 4 = 17.92' 1,010,135 ft. 3 Using Morrish's formula: KB = 1/3 (5/2 xT-S = 1/3 (5/2x29) - df' '' 3 * ) A 96.7 x 420 KB = 1/3 [72.5 -24.87] = 15.88' KM = KB + BM = 1 5.88' + 1 7.92' = 33.80' Hydrostatic properties (page 6 of 68c T&S book) shows a KM of 33.68' for a draft of 29'. Explanation of vertical movement of transverse metacenter: Most container and barge type carrying vessels in a light condition are particularly stiff. This means a large value of GMt. The change in the vertical position of B is directly related to the change of draft. In a full formed cargo vessel about 0.50' increase in KB for each 1 ' increase in draft. The great value of KM at light drafts therefore must be due to a greater value of BM. At low drafts, the ratio for I/V is large. As the drafts increase the I increases at a slower rate than the V, leading to a decreasing I/V ratio. The curve of KB is nearly a straight line. This leads to the assumption that the increase in KB has almost a direct ratio with the increase in draft. The curve of KMt decreases slowly at light drafts, then is almost constant throughout its length and finally at the deepest drafts may increase slightly. Effect of trim on KMt. The extreme trims that are possible in the operation of container and barge carrying ships have an effect on KMt. At the present time most T&S books make no effort to correct for this trim. Some curves of form have curves of change in displ. and KMt for trim. It appears likely that the USCG will insist on this data being included in future barge and container carrying ship's T&S books. 11 Some rule of thumb ratios for full formed cargo ships are as follows: Gain in KM for trim by the stern .04' of KM/1 'of trim Loss in KM for trim by the bow .02' of KM/ 1' of trim For change in KM due to trims less than 5'— .1 x B 2 x trim d L where B = beam d = draft L= length of W.L. Questions: Page 47 of Stability and Trim for the Ship's Officer by La Dage and Van Gemert. Questions 1, 3, 4, 9, 10, 1 1 , 14 Problems: Page 48 of Stability and Trim for the Ship's Officer by La Dage and Van Gemert. Problems 2,4,5,6,7,8, 1 1 CALCULATION OF GMt The metacentric height GMT is a measure of initial stability and is a standard that we must meet in loading, discharging, ballasting, deballasting, storing or consuming stores, or any combination of these operations. It is shown in the T&S book as required GMt vs. draft and is a criteria that must be met through out the life of the ship, at sea and in port. GMt, however, is a measure of initial intact stability, it is not stability. At all angles of inclination the measure of stability is (GZ) the righting arm. The only true meaningful standard of stability for all conditions is the righting moment. GMt is a function of the righting moment. GMt and amplitude, determines the speed of roll. M is a fixed point at a constant displacement for inclinations up to 7° - 10°. As we lower G and increase GMt at a fixed displacement we increase (GZ) the righting arm and righting moment. The T&S book will show a GMt required vs. draft curve. This curve must be met in all loading conditions. The GMt may be calculated as follows: KMt-KG = GMt The GMt curve may also be checked by measuring the rolling period but we will cover this in a later chapter of the text. Questions: La Dage & Van Gemerts, "Stability and Trim for the Ships Officer." 12 Page 29 Questions 3, 5, 9. Problems: La Dage & Van Gemert's, "Stability and Trim for the Ships Officer." Page 30 Problems 2, 3, 8. FUNDAMENTALS OF TRANSVERSE STABILITY When any body is in equilibrium in such a manner that if when displaced slightly in any way it returns of itself to its original position the equilibrium is said to be stable and the condition is said to be one of positive stability with respect to its original position. Specifically stability is the tendency of a ship to return to the original position when inclined away from that position. A freely floating undisturbed body in a still liquid is acted upon by 2 resultant vertical forces the upward force of bouyancy and the downward force of weight. The resultant of the bouyant forces of the liquid can be considered as a single force applied vertically upward through the center of bouyancy and the resultant of all the weight is a single force acting vertically downward from the center of gravity. If the body is at rest in equilibrium the resultant forces must be equal and opposite and the center of bouyancy must be in a vertical line over and in line with the center of gravity. If the body is displaced so that the center of bouyancy Bi is not in a vertical line directly over or under the center of gravity G the body will not remain in that position but will move to a position such that the above conditions necessary for a body to remain at rest are fulfilled. It may help to visualize the equilibrium of a ship by comparing it to an ordinary "rocking chair". G is the combined center of gravity of chair and occupant. B corresponds to the "center of buoyancy" M is the center of curvature of the rocker and is the "metacenter" of the chair or the point that B stays under as the chair rocks. B 1 corresponds to the "center of buoyancy" shifted BM corresponds to the "metacentric radius" BM corresponds to the "metacentric height" GZ corresponds to the "righting lever" M must be above G for the chair to be stable. If one stands on the chair and grasps the back so as to bring the combined "G" higher than "M" the chair will capsize. 13 B FIGURE 7 What happens when a ship heels is as follows: Assume the ship heeled over to waterline W ( L x ; "G" remains in its original position but due to the shift of a wedge of bouyancy from the emerged side of the ship to the immersed side "B" shifts transversely, as in the rocking chair such that a righting lever of GM sin 6 is developed and the ship will return to the upright position when the righting moment (GM sin 6) exceeds the heeling moment. This of course assumes that "G" is below "M" (GM positive). If the center of gravity were to be at the point "M" (or above), no righting lever would develop on heeling and the ship would be unstable and would not return to upright if heeled over by some external force. What happens when a ship heels as a result of outside influences or on board forces see sketches on the following 2 pages. INCLINING EXPERIMENT FIGURE 8 The ultimate determination of Center of Gravity (KG), Metacenter, and Lt. ship Displacement will be as a result of an inclining experiment. 14 "Inclining Experiment" We know that the weight of the ship acting downward through the Center of Gravity (G) and the bouyancy acting upward thru the "Center of Bouyancy" (B) are equal and opposite forces. If we were to shift some weight transversely such that the "Center of Gravity" is moved off the C/L plane, the ship must heel to an angle where the forces are again in balance and the righting moment is equal to the heeling moment. If the heeling moment is W x d and the righting moment is Displacement x GM sin 6 we can equate these values such as:- W x d = Displacement x GM tan 0, or GM W x d Displacement tan 6 and this is the formula used when conducting the inclining experiment. W is the inclining weight d is the distance it is moved 6 is the angle of heel The displacement is that measured at the time of the experiment. All of the preceeding discussion is related to small angles of heel up to about 1 0° and applies only when the deck edge is not immersed. CENTRIFUGAL FORCE EFFECT OF OUTSIDE WEIGHT FIGURE 9 EFFECT OF A TURN FIGURE 10 15 FIGURE 11 EFFECT OF GROUNDING WIND PRESSURE FIGURE 12 EFFECT OF WIND AND WATER LIFTING A WEIGHT OVERSIDE FIGURE 13 16 To Review Stability is positive when "Center of Gravity" (G) is below the "Metacenter" (M). This distance be- tween these points is called GM (transverse). A-3 STABILITY AT LARGE ANGLES OF HEEL Righting Arms— The righting arm may be described as the distance between the line of force thru Bj and the line of force thru G when there is positive stability. GZ is called the righting arm and for small angles of inclination is calculated as follows: GZ = GMtsinfl The righting moment or the force working against the heeling moment is — displ in tons x GM sin 6 FIGURE 1U The righting moment is the true measure of the stability of the vessel. At angles larger than 10° the effect of the form of the ship causes the center of buoyancy to shift such that the metacenter (M) does not remain in one place. The righting lever must then be determined by actual integration of the hull form at the various angles rather than by calculation of the moment of transfer of the wedges of figure 14 as is the case for small angles. A typical righting lever diagram for a conventional ship could be as shown here. 17 Since the sine of the angle closely approximates the angle in radians for small angles of heel, we can draw a line from zero to the GM value at 1 radian (57.3°) and this line represents GM sine 6. The righting lever can then be considered to consist of GM sin 6 plus a correction for the form of the ship. FT FIGURE 15 ANGLE OF HEEL PLOT OF RIGHTING LEVER VS HEEL Questions: La Dage & Van Gemert Chapter 1 page 1 1 questions 6, 7, 8, 10, 11, 15, 16. Curves of Statical Stability: In the operation of ships at sea it is necessary to estimate the stability of vessels at large angle inclinations. It is basically an evaluation of the force that the vessel exerts in returning to the upright. This righting moment a function of the couple expresses in foot tons the force that will be exerted to right the ship. Therefore, it is essential to know the righting arm at all times. This information is available on the Statical Stability curves which, if not on ship, should be obtained from the owners of the ship. These curves are drawn for a range of displacements. Each curve is for one displacement and is plotted as righting arm versus angle of inclination. An assumed constant KG is used in calculating all righting arms and is chosen low enough to give a positive value of righting arms through the range of stability. Correction to righting arms for difference in G (Assumed G versus Actual G) GG' sin G = assumed G G' = actual G sin 6 = angle of inclination If actual G is above assumed G, the correction to righting arm is subtractive. If actual G is below assumed G, the correction is additive. Correction to righting arms for transverse shift of G This correction is subtractive as follows: Lost righting arm = GG' cos 6 18 CENTER OF GRAVITY ON CENTER LINE CENTER OF GRAVITY OFF CENTER LINE LOST GZ = GG' cos 8 .'.G'Z's GZ-GG 1 cos 6 FIGURE 16 STATIC STABILITY CURVES 40° 50° ANGLE OF INCLINATION KG ASSUMED TO BE 21.0' eo 1 70° 80 ( w FIGURE 17 19 Correcting the Stability Curve— graphically GG* = 2.0' GZ KG 25' 10 NEGATIVE GZ's 20 30 u 40" FIGURE 18 60 l 70 v 80 l 90 l Righting Arms corrected for KG 2.5' higher than assumed and located 2.0' off C.L. Note: new baseline is the cosine correction curve Some data on Stability Curves 1 . The angle at which maximum righting arm is developed is intimately associated with the angle at which the deck edge is immersed. For cargo vessels deck edge immersion can be considered for practical purposes as the end of the range of stability, since after that angle is reached the value of the righting arms decreases rapidly. 2. Increase of freeboard results in larger values of righting moment at all angles of inclina- tion beyond the angle of deck edge immersion. 3. Tumble home results in a loss of GZ at all angles after immersion of the tumbled portion of the side. 4. As displacement increases, the righting arms on the curves show a gradually decreasing tendency. 5. Curves of statical stability should be studied carefully because they assume stability in still water and they ignore ship motions and wave action. 6. It should be remembered that these are curves of righting arms not righting moments. 7. A curve showing large values of righting arms at light displacement does not necessarily indicate more stability than a curve showing smaller arms at a larger displacement. Questions: In Stability and Trim for the Ship's Officer by La Dage and Van Gemert consider these questions on page 88: — 1,2,3,4,8, 12, 13, 14, 15 20 Cross Curves of Stability Cross Curves are used to find the value of righting arms just as Statical Stability Curves are used to find the same thing. In Cross Curves the angles of inclination are constant and the displacement changes. The Statical Stability Curves are the opposite of this. Both methods produce identical righting arms for the same displacement, inclination and KG. The curves are corrected in the same way. It might be noted that the cross curves and statical stability curves can be considered as forming a three-dimensional system and that the statical stability curves can be formed from the cross-curves. 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USCG WEAT HER C 3 ITER IA i— 26 UJ UJ V i cr Q 24 \ \ '\ O UJ Q _) o \ \ 1 \ \ 1 \ 21 _l 22 \ 1 \ Y \ \ 1— z: i i i i \ j\ |\ i \ 1 \ \ 20 1 \ 1 \ \ \ ! \ \ | \| \ \ 1 i 1 ; \ -® ■ 18 1 1 \^(2)\ i 1 I 1 1 1 ! 16 ! 1 i 1 ? I i | REQUIRED i GM- FEET i I \ 1 i 1 1 1 ! DAMAGED STABILITY-CURVES OF GMt REQUIRED vs DRAFT FIGURE 32 61 FIGURE 33 CURVES OF AVAILABLE S REQUIRED GU-FEE1 62 FIGURE 3$ FIGURE 36 //. 'sB Items located within a distance '/$ f Beam from ships side FIGURE 3U V. W i ng Tanks ™.. WBom/i/mm. _y__t H e i 9 h t of flat 63 FIGURE 37 Large waterplcne area with unc re s s connected tank _ be I ow FIGURE 38 Longitudinal extent of damage Arrg" t inciudit g compartmen t s or store spaces that are watertight Large sa i i area above W'L FIGURE 39 64 Uncross connected tank s FIGURE hO 65 TRIM & STABILITY BOOK PART 11-14 INSTRUCTIONS & ROUTINE OPERATING INSTRUCTIONS The Trim and Stability Book is approved by U.S.C.G. and the Maritime Administration. In effect it is the deck officer's bible as regards the operation of the ship. It is a complete entity and contains data from the Lines, Inclining Test, Deadweight Certificate, Capacity Plan, Hydrostatics, Tank Capacity Table, Intact Trim and Stability Calculations, and Damaged Stability Calculations. It will also contain data from U.S.C.G. Regs., and National Cargo Bureau Regs. Basically the book is composed as follows: Index Vessel Characteristics Instructions — General — Computation of Vessels T&S (long form) " " T&S. (short form) — Routine Operating — Special Cargoes — Calc. of VCGs of Deck Cargo Table of Hydrostatics Trim Table and Example Table of Approx. Gain in G.M. by Ballasting Tanks Composite Curve of GMt Required Tank Capacity & Free Surface Data Cargo Space Capacity Table Typical Loading Conditions (long form) Nomogram — Short Form Short Form Example One of the more important parts of the book is the section in the beginning marked "Instructions". The Instructions are in effect the ground rules under which the ship will be operated. The "Instructions" will be tailored to the particular ship and will be checked very closely by the U.S.C.G. and MarAd, as will the rest of the book. Some of the highlights of typical container ship instructions are as follows: 1 . Instructions are intended to aid personnel in maintaining satisfactory stability. 2. Cargo conditions shown in book represent cargo loadings having similar tonnages and VCG's to those shown. 3. Long form used for calculating vessel's trim and stability shall list commodities listed on tables shown on specific pages. 4. Slack free surface shall be entered for the settlers. 5. Slack free surface entered for the consumable liquid storage tanks shall result in a sum not less than the tank pair values which are the largest for each type of consumable liquid being used. This will allow tankage to be consumed in any order. 66 6. All other 98% full fuel tanks shall have 98% - 5° heel free surface values entered. 7. In the separate loading tables each category is summed with respect to tonnage, vertical moment, longitudinal moment, and free surface. 8. Mean draft equivalent to displacement is used to enter table of hydrostatics to determine KM, LCF, and LCB. 9. Vertical and longitudinal centers of gravity of containers are as shown on the container loading table. 10. Cross connections between all port and starboard double bottom and deep tank pairs shall be kept closed when carrying liquids, and open when empty. 1 1 . Excluding the fuel oil settlers not more than one pair of tanks assigned to each type of consumable liquid on board the vessel shall be slack at one time. 1 2. Bilges shall be kept pumped to minimum content at all times. 13. Tanks required to be ballasted with salt water shall be immediately filled and carried pressed up at all times. 14. When not ballasted such tanks shall be kept pumped to minimum content at all times. 15. During the ballasting a reduction in the vessel's GMt due to slack free surface will occur until the tanks are pressed up. This temporary loss in GM (in feet) is equal to the salt water free surface of the tank divided by the vessel's displacement (in cubic feet) at that instant of loading. 16. When the available GMt calculated by the short form method comes out less than the required GMt three alternatives shall be used to correct this condition: a. Check by the long form method. Then if the available GMt is still less than the required GM, use either of the following corrective measures: b. Add ballast where available. c. Add ballast as required and then fill the roll stabilization tanks to suit displacement and GMt of the vessel. Conclusions: I. Avoid excessive GM (transverse). In other words, load the ship with enough GM to give a slight margin over GM required, but not more than this. This may lead to a GM slightly less than given by the GM available plot, but as long as it is not as low as the GM required we have not in principle, jeopardized the ability of the ship to survive damage, and we should have reduced the likelihood of severe rolling somewhat. II. Unless there is guidance to the contrary in the trim and stability book, load the heaviest containers in the middle of the ship, and the lightest ones at the ends. This should help reduce the likelihood of severe pitching somewhat, by reducing the longitudinal radius of gyration. These conclusions were extracted from "Guideline for Deck Stowage of Containers" produced by J.J. Henry for the Maritime Administration. Texts: U.S.C.G. sample Trim & Stability Book C7-S-68d Trim & Stability Book C5-S-73b Trim & Stability Book C8-S-81a Trim & Stability Book 67 Questions: 1 . What do the instructions state in regard to GMt values? 2. What is the purpose of the T&S book? 3. What type of free surface is entered for fuel oil settlers in calculating vessel stability? 4. What should the sum of the slack free surface of the consumable liquid storage tanks be not less than? 5. What free surface shall all fuel oil tanks (that are not slack) have entered for them? 6. What instructions are given for cross connections? 7. Excluding the fuel oil settlers, how many pair of tanks assigned to each type of consumable liquid may be slack at one time? 8. When the available GMt as calculated by the short form method comes out less than that required what 3 alternatives are available? 15 TANK CAPACITY & FREE SURFACE TABLE Explanation of Table This table in its simplest form is laid out to contain the following: Name of tank Location (frames) Capacity (ft. 3) Capacity (tons)/liquid V.C.G. L.C.G. from amid ships or F.P. Free Surface— slack for all tanks Free Surface-98%-5° heel for fuel oil and cargo oil Free Surface for flume tanks is at operating level In the case of container and barge carrying ships with extensive tankage the tanks are generally grouped in the table by the liquid they will carry as follows: Salt Water Ballast tanks Fuel Oil and Diesel Oil tanks Fresh Water tanks Liquid Cargo tanks Miscellaneous tanks 68 Flume Tank Free Surface Diagram An adjunct to the free surface table is the Flume Tank Free Surface Correction diagram. This is based on the flume tank's free surface correction vs the level of liquid in the tanks. The level of liquid in the tanks is shown vertically. The moment of free surface in foot tons is shown horizontally on the bottom of the diagram. The free surface is shown as actual moment and maximum effective moment. Maximum effective moment is based on the U.S.C.G. method of calculations. Actual moment is based on full free surface calculated as the moment of inertia of the liquid free surface. The table of capacities and free surfaces will show a free surface correction in the slack condition that will be more conservative than will be read on the diagram. Use of Table 1. The table will be used to provide V.C.G., L.C.G. and free surface values for tankage as input in long form trim and stability calculations. 2. To provide tank tonnage as input for short form trim and stability calculations. 3. To provide tank tonnages as input for calculating trim by the use of the trim table. Bibliography: 1 . U.S.C.G. sample Trim & Stability book 2. C7-S-68d Trim & Stability book 3. C8-S-81b Trim & Stability book 16 GAIN IN GMt BY BALLASTING - TABLE The "Gain in GMt by Ballasting Table" is one of the handiest and most useful tables in the Trim & Stability Book. Basically the table is as follows: The tanks are listed horizontally. The displacement is listed in even increments vertically. The results are the increase or decrease in GMt in terms of feet of GMt. In working up the table a base KG is derived from the difference between required GMt curve and the KM taken from the hydrostatic table in the T&S book. Specific displacements are chosen and the effect of ballast tanks on the KG are calculated. It should be stressed that this is only a guide and should not be used as a shortcut measure to determine the available GMt of a ship. Using the C7-S-68d Trim & Stability book turn to the "Gain in GMt by Ballasting table". What will the gain in GMt be if we ballast #3 ^ double bottom tank in the "Arrival— No Cargo— 10% 69 FREE SURFACE CORRECTION = MOMENT OF FREE SURFACE (SUM OF TANKS USED) DISPLACEMENT (A) 10 9 _ AFT FLUME TANK MAXI- MUM EFFECTIVE MOMENT 20,943 FOOT-TONS 7 _ MAXIMUM EFFECTIVE MO- MENT USING COAST GUARD METHOD OF CALCULATIONS 5 _ 4 _ FWD FLUME TANK MAXI- MUM EFFECTIVE MOMENT 20,804 FOOT-TONS 2__ AFT TANK ACTUAL MOMENT FWD TANK ACTUAL MOMENT 0.000 FIGURE U1 1 1 I I 5,000 20,000 25,000 30,000 MOMENT OF FREE SURFACE-FOOT TONS 35,000 FLUME TANK FREE SURFACE CORRECTION 70 Consumables" condition. This condition has a displacement of 16,299 tons. Double Bottom #3 ^ has a 1 00% capacity of 473 tons of SW. If we enter the table with this displacement and tankage we arrive at a gain in GMt of 0.48'. Precaution: Before starting to ballast certain facts must be considered: a. What is the present GMt? b. What is the GMt required? c. What is the slack free surface correction for the tank to be ballasted? d. What will the trim be as a result of ballasting? Solution: a. The present GMt may be calculated by long form or short form. b. GMt required may be read from "Curve of GMt Required vs Draft". c. Slack free surface correction is read (because it will be maximum) from table of tankage. d. Trim is determined from trim table. Reasons: a. GMt of ship should be known at all times. b. GMt required should be known to determine if ship has required stability. c. The free surface should be known to determine what condition the ship is in during the ballasting. Problems 1. Using C7-S-68d Trim & Stability Book determine what effect deballasting #2 double bottom <£ tank would have on available GMt, in Arrival Full Cargo, 10% Consumable condition. 2. Using C7-S-68D Trim & Stability Book determine what effect deballasting would have on available GMt in Arrival - No Cargo, 1 0% F.O & Stores condition. 17 TRIM TABLE Explanation of Table This table is extremely handy for solving trim problems. It is designed to show the changes in drafts at the forward and after draft marks. The table is worked out for two mean drafts. Interpolation is required for mean drafts in between these drafts. The table is located below a profile of the ship and is laid out for even increments of distance. Below these distance marks are boxes showing the 71 change in draft at the forward and after draft marks. These changes in draft marks are marked with a plus or a minus sign. The table is laid out for loading a specific weight (generally 100 tons). When discharging the same changes in drafts are used but the signs are reversed. The changes in drafts are shown in inches and decimal parts of an inch. If adding or removing large amounts of weight from ship more exact results are obtained by using long form. Example: On the C7-S-68d S/S AMERICAN LARK in the "Departure - No Cargo, Full Consumables"-condition 450 tons is loaded in #8 hold at a point 80' aft of M.P. The drafts at the marks before loading were 24' 1/8" aft. and 17' 2 7/8" fwd. What was the change in drafts due to this operation? Change in Marks as Calculated LCF 339.1' aft of F.P. 4.15.0 ' aft of F.P. —cargo loaded at 76.1' lever MT1" 2690 ft. tons trimming moment 76.1' x 450 tons = 34,245 ft. tons total trim = 34,245 = 1 2.73" 2,690 distance between draft marks 638.0' trim at fwd. marks .522 339r+x 12.73" =-6.64" 63&r0 trim at aft marks = 12.73" - 6.64" = +6.09" TP1" = 88.9 sinkage = 450 =5.03" 88.9 change in drafts Fwd. = +5.03" - 6.64" = - 1.61" Aft. =+5.03" + 6.09" = + 11.12" Change in Marks as Per Table Fwd. drafts 17' 2 7/8" Aft, drafts 24' 1/8" Mean draft 41' 3" = 20' 7 1/2" use table for 20' mean draft at a point 80' aft of M.P. change in fwd marks for loading 1 00 tons = - .3" change in aft marks for loading 100 tons = + 2.5" 72 change in fwd marks for loading 450 tons = - .3" x 4.5 = - 1 .35" change in aft marks for loading 450 tons = + 2.5" x 4.5 = +1 1.25" using the table we are able to come up with changes in drafts of - 1 3/8" fwd vs. - 1 5/8" fwd calculated and + 11 1/4" vs. + 1 1 1/8" calculated at the aft location. Uses of Table There is no substitute for calculating the change in drafts but this table gives a very close approximation of the change in drafts. This table may be used to determine drafts in the following operations: Loading Discharging Ballasting Shifting liquids Departure draft problems Arrival draft problems Questions: Using the C7-S-68d Trim and Stability Books solve the following problems: 1. In the "Departure - Full Cargo, Full F.O., Full Stores" condition (page 15) if the following tanks were deballasted #1 D.B.CL #3 D.B.Cl #3 D.B.P&S #4 D.B.CL #M-1 D.B. What would the new drafts be? What would the change in GMt be? 2. In the "Arrival— Full Cargo, 10% Consumables" condition if the containers on deck were discharged? What would the new drafts be? 18 HYDROSTATICS TABLE The "Hydrostatics Table" is an essential part of the Trim and Stability book. Because the book is a complete entity it must contain sufficient data so that loading, discharging, ballasting, deballasting and liquid transfer problems involving trim, stability and capacities may be solved without reference to other plans, booklets or tables. 73 The table of Hydrostatics is included to circumvent having to use a "Curves of Form" plan. The table is laid out with the drafts and data laid out vertically. The table is split into columns. Horizontally across the top of the page is the title of the columns. The mean keel drafts are the extreme left and right columns. The columns in between will contain the following data: Deadweight— salt water— long tons Total Displacement— salt water— long tons Transverse Metacenter above base line— KMt in ft. (Total) Tons Per Inch— salt water— long tons Moment to Change Trim one inch— foot tons Longitudinal Center of Buoyancy— aft of F.P.— feet Longitudinal Center of Flotation— aft of F.P.— feet This in general will be the data contained in these tables. The table will be tailored to the ship and its operation. Some of the additional data can be as follows: Change in Displacement for 6' trim— aft Change in Displacement for 12' trim— aft Change in KMt for 6' trim— aft Change in KMt for 12' trim-aft The table is used by laying a straight edge across between the outboard mean keel draft columns. Read down the appropriate column and read the data at the point where the straight edge cuts across the column. Bibliography -C7-S-68d Trim & Stability Book. C8-S-81b Trim & Stability Book, U.S.C.G. (sample) Trim & Stability Book Problems: 1. The C7-S-68d in the arrival— Full Cargo— 10% consumables condition has a displacement of 29,35 1 tons. What will the Tons Per Inch be at this displacement? 2. If the ship in question 1 has a KG of 31.85' and a displacement of 29,351 tons and the following S.W. Ballast tanks (100% full) are deballasted: #1D. B. P&S 336.6 tons 2.7 ft. VCG #2D. B. I— ZONE 5 FIGURE U8 92 c. The scale divisions are linear and should be chosen on the basis of convenient length of line for reading and the range of the scale. The subdivisions of the scale should be decimal. Stability Factor Scale— The right hand line will be the scale of stability factors. The calibration of this scale is based upon the following considerations: a. The upper intersection is always the zero reference point for the scale. b. The range of the scale is based on the maximum anticipated stability factor which can be generated for the particular zone. A few check calculations varying x in the following equation will identify the maximum stability factor: Stability Factor = (x tons loaded) x (zone lever) (basic ship displ.) + x c. The scale calibration is linear and decimal. The sign of the stability factor must be clearly noted. Displacement Scale— The canted line will be the scale of displacements. Its calibration is non linear and is not selected but derived: a. The range should extend from lightship displacement to full load displacement. b. The calibration is accomplished by solving the basic equation for a specific set of variables and then using the left and right scales as references to plot the solution, thereby establishing a discrete point on the displacement scale. Additional displacement marks are obtained by repeating this process. Presentation: The calculated data is presented in the Trim and Stability Booklet as follows: — Instruction sheets Short Form calculation sheet Basic GMt tabulation sheet Nomographs Short Form example Short Form Calculation Sheet a. Separate cargo or liquids actually loaded into appropriate zones with provisions for the departure and arrival conditions. b. Use Deadweight Summary Table for various conditions. Enter total tonnage into appropriate zones. Enter the appropriate stability factor for tonnage loaded in each zone. Determine algebraic sum of stability factors. c. Summarize Displacement by summing Basic Ship Displacement (a constant) and total deadweight in the specific condition. d. Record departure and arrival mean drafts in appropriate spaces. 93 e. Summarize stability in appropriate spaces with regard to the following: Basic GMt Net Stability Factor Available GMt Required GMt Basic GMt Tabulation Sheet— Basic GMt is read off for appropriate displacement and mean draft. Nomographs are provided for each zone. (Different nomographs may be provided for the same zone for different cargoes whenever this added refinement is considered beneficial) Conclusion— This has been a rather lengthy detailed section of the course. The ability to use the Short Form is the very essence of utilizing the Trim & Stability Book in fast turn around container and barge carrier operations. It is good to remember that the results obtained with the short form will not necessarily agree with the long form because of minor variations between actual and assumed values of items contained in basic displacement. Problems 1. Using C8-S-81b Stability Booklet and by means of Short Form method calculate Total Displacement, GMt (uncorrected), Free Surface Correction, available GMt, Required GMt, Drafts at Marks for following conditions: — a. Departure 100% Cargo, 100% Consumables b. Arrival 100% Cargo, 10% Consumables c. Departure 50% Cargo, 100% Consumables d. Arrival 50% Cargo, 10% Consumables e. Departure 0% Cargo, 100% Consumables f. Arrival 0% Cargo, 10% Consumables Bibliography 1 . U.S.C.G. Navigation and Vessel Inspection Circular No. 3-69-Z Nomograph Method of Calculating Available GMt. 2. C8-S-81b Trim and Stability Booklet 3. C7-S-68c Trim and Stability Booklet 4. U.S.C.G. sample Trim and Stability Booklet 94 PROBLEM SOLUTION PART III -24 MECHANICAL & ELECTRONIC STABILITY & LONGITUDINAL STRENGTH CALCULATORS Stability, trim, and longitudinal strength are real problems on container and barge carrying ships. The reasons for this are the following: 1 . Quick turn around. 2. All containers & lighters look the same— the loading can no longer be eyeballed i.e., 2/3 in the lower hold, 1/3 in the tween decks. 3. The loading is vertical i.e., not all holds working simultaneously but each hold in turn being loaded vertically. 4. These ships almost always have deck loads and in the Full Load Arrival condition stability is frequently marginal. 5. Utilization of flume tanks requires accurate stability data at all times throughout the voyage. 6. Draft and trim data will have to be accurately known to sail into newly developed container & barge terminals where the channels have been dredged or artificially created. Some of the methods of calculating stability, draft, trim, and longitudinal strength other than by hand calculations and nomogram are the following: 1 . Stabilogauge— American Hydromath Co.— mechanical/electronic. 2. Trim & Stability Calculator— Sperry Rand— electronic. 3. Shore Based Computer System— Hydronautics. 4. Stalodicator S5-Gotaverken— electric. There are other mechanical and electrical methods of performing these calculations and new devices are sure to be forthcoming in the future. The above devices and systems are known in this country at this time and cover a broad spectrum of methodology. Stabilogauge— Most ship's officers are familiar with this device. They have generally been involved with them in their careers. Basically this device is a calculating device, rectangular in shape, mechanical in operation with micrometer dials and gauges with movable pointers. Each stabilogauge is tailored to a specific ship or class of ships. 95 The "Stabilogauge" instantly determines the mean draft, displacement, deadweight, and stability which the ship will have under any condition of loading or at any time during a voyage. The actuators (thimbles) are set to the actual condition of loading and the indicators on the gauges show mean draft, displacement, deadweight, metacentric height (GMt). The actuators on the right side are set to represent total loading on a level. The actuators on the left side are set to correct for free surface, and density. The GMt as read from the gauge if it is not adequate for damaged stability will be accompanied with a red flag. Trim & Stability Calculator— This is an electronic device designed by Sperry. Like the Stabilogauge it is tailored to a specific ship. This device is set in a stand up console. On the front of the console is marked a profile of the specific ship laid out for compartments, levels, tanks, double bottoms, store rooms etc. In each of these spaces is located a potentiometer. In the case of spaces that could have a free surface a 2nd "pot" is located. The loading including density and free surface corrections is accomplished by turning the "pots" to the equivalent loadings and corrections. This device will produce the following results: Draft trim displacement deadweight GMt sheer bending moment Shore Based Computer Program— This is a computer program located at a shore installation. It was designed specifically for container ships. The computer determines and regulates the loading. The computer program will also furnish required information through out the voyage by means of data forwarded by radio. The results are then transmitted back to the ship in the same way. The discharge and loading operations in the out ports may also be controlled in this way. This device will produce the same results as the previously mentioned devices. There is one distinct advantage however because when a computer is used the absolute optimum loading plan can be generated. The program is capable of generating infinite combinations of loading until the optimum loading plan has been reached. Stalodicator S5— This instrument is designed specifically for containerships. It is basically an electric or electronic calculator. It has no connection to the ships hull and does not measure actual stresses. The instrument is fed with data concerning the loads in the ships holds, tanks, and store rooms. It gives a reading that indicates how the cargo, tankage and stores distribution will affect the hull. The instruments are based on a simple principle (the Wheatstone bridge). The components consist mainly of fixed and variable resistances. There are no moving parts except the knobs for plugging in the loads. Each instrument is tailored to a specific ship or class of ships. Each vertical container section in the ship is represented by a knob, while the horizontal tier of containers is represented in a special part of the apparatus designated "Section Calculation." The ship's officers set up on these knobs the tons of cargo allotted to each horizontal tier. The instruments gives an accurate indication of the moment for each section and these are transferred to the main section of the instrument. Weights of bunkers, ballast and stores are also fed into the instrument, together with corrections for free surface in tanks. 96 The Stalodicator S5 provides information as to draft, trim, deadweight, bending moment amidships and stability. The Stalodicator can readily be adapted to other uses. Some container ships have shipboard cranes which frequently will not operate satisfactorily at excessive angles of heel. The Stalodicator can be employed to indicate the maximum load that may be lifted by a crane without causing a predetermined angle of heel to be exceeded. Also, a check can be made to ensure that a proposed lift is within the safe stability limits for the ship. Summary— Lighter and container carrying ships are turning to mechanical and electrical devices because of the following reasons: 1 . quick turn around— shortage of time 2. use of flume tanks to keep ships from being too stiff— (stability must be known when tanks are operated) 3. minimal stability available in "Full Load Arrival" condition 4. longitudinal strength is a problem 5. ship based cranes are limited as to working efficiently when ship has a heel. 6. stability available to limit heel must be known under all conditions. Questions 1 . Which devices electric or mechanical has greatest reliability? 2. What is the advantage of shore based computer program? 3. What does Stalodicator S5 do that other shipboard devices do not do? 4. What special problem do lighter & barge carrying ships have in common with tankers? 25 PROBLEMS OF SHIP OPERATION The Trim and Stability book is an instruction book and a tool. It provides a concentrated source of data for ship operation. It is also a tool that is to be used in problems that arise in ship operation such as: loading cargo -effect on trim, draft, stability, longitudinal s + rength discharging cargo -effect on trim, draft, stability, longitudinal strength ballasting- effect on draft, trim, stability, longitudinal strength, rolling period changing— rolling period— increasing or decreasing stability 97 The trim and Stability Book is also an instruction book with instructions in the following areas: computation of vessel's stability and trim, long form and short form cross connection — instructions slack tanks — number permissable bilges— condition of at all times temporary reduction in GMt — during ballasting The Trim and Stability Book is also a source of data such as: light ship data permanent ballast data trim table ~ tank capacities and free surface table GMt change due to ballasting cargo stowage data tables sample loading conditions— long form short form -nomographs All of the above information and data has been covered throughout this text. All that is intended here is a review before we start to solve problems utilizing all of the information in the Trim and Stability Book singly and in combination. Problem 1 If the U.S. Lines S/S American Legion (C7-S-68c) is in the Arrival-Full Cargo- 10% Consumables condition, determine how much ballast can be dumped before arriving in port and still remain stable. a. If all liquid ballast was removed, how many 8 ton containers may still be carried on deck? b. If the Roll Stabilization Tanks were dumped, what effect would this have on the stability in Arrival-Full Cargo— 10% Consumables— condition? c. What would the drafts be if all liquid ballast was removed and Roll Stabilization Tanks were emptied? Problem 2 The S/S American Legion (C7-S-68c) leaving New York with Full Fuel Oil, Full Stores, and containers stowed in the tiers 1, 2, 3, and 4 the same as shown in the Full Load Departure condition i.e. 1 12-20' containers @ 12 tons each and 142-40' containers @ 24 tons each. The ship is bound for Baltimore to finish loading. Determine the quantity of liquid ballast needed to meet GMt required with a margin of 0.17'. Determine drafts and keep trim within 2'-4' by stern. Use extra ballast, if necessary. Problem 3 A C5-S-78a class vessel has loaded 222-40' containers at 25 tons each. The loading is as shown for the 25 ton containers, 100% Cargo Oil and 100% Consumables except that 103 containers on deck 98 and the cargo oil will be loaded in Philadelphia. When leaving New York, it is desired to be as close to even keel as possible. Determine the following: stability draft trim longitudinal strength numeral and the amount of salt water ballast required to meet the above conditions. Problem 4 A C5-S-78a class vessel is departing from her last foreign port in the Full Load Condition with 325-40'-25 ton containers and 100% cargo oil. Upon arriving in New York she will have 10% consumables. How many containers would have to be left on the dock and where would the balance of containers have to be stowed so that only 1,500 tons of salt water ballast stowed to advantage would result in a stable ship with 2'-4' trim by stern and a longitudinal strength numeral of less than 100. Problem 5 The S/S LASH ITALIA (C8-S-81b) has the following loading conditions shown in the Trim and Stability Book: 100% Cargo - Departure 100% Cargo -Arrival 50% Cargo - Departure 50% Cargo - Arrival 0% Cargo - Departure 0% Cargo - Arrival All of these loading conditions are shown in the long form. Check these loading conditions by the short form and compare stability results. Problem 6 The S/S American Lancer C7-S-68c is arriving in port in an "Arrival-Full Cargo- 10% Consumables" condition. If the Roll Stabilization Tanks were dumped and all Fresh Water Tanks were pressed up, how much could the Salt Water Ballast be reduced and still have a stable ship? Problem 7 The S/S American Legion C7-S-68c leaves Baltimore in the Full Cargo 1 0% Consumables condition. On the first day at sea the outboard 3 rows of containers on the 3rd tier on top of holds #4 and #5 are swept over the side. Assume the 18 containers are 28' off center line and the vertical center of gravity of containers is 67.5' above the base line. Assume weight of containers are 8 tons each. 99 a. What will the heel be as a result of the loss of the containers? Problem 8 A Moore McCormack C5-S-78a ship is loaded with containers at a weight of 18 long tons each, 100% cargo oil and 10% consumables (as shown on Page 76). a. What is the rolling period in this condition? b. What will the rolling period be if the Anti Roll tank is dumped? Problem 9 The C6-S-1 w class ship the "S/S American Leader" is departing in a Ballast Condition with 1 1.31' of trim by the stern. a. What is the rolling period in this condition? b. How much can we reduce trim by pressing up empty clean ballast tanks and fresh water tanks? c. Determine the new KG, GMt, and rolling period. Problem 10 The C6-S-lw class ship the "S/S American Leader" has permanent ballast stowed in the lower holds. If this permanent ballast was removed, could the ship carry containers on deck in the 100% Cargo-100% Consumables departure condition and still meet the stability requirements. If not could the ship carry a reduced number of containers and if so how many? Bibliography: C6-S-lw Trim and Stability Book C7-S-68c Trim and Stability Book C5-S-78a Trim and Stability Book C8-S-81b Trim and Stability Book 100 PENN STATE UNIVERSITY LIBRARIFC 111111111111 AQQ0Q712L533T