Interaction of Ships while Opposing Navigation among Small Ice Floes

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1 ARCTIC OI RECOVERY EXERCISE 05 KEMI ARCTIC 05 Conference Interaction of Ships while Opposing Navigation among Small Ice Floes Vadim K. Goncharov Professor Department of Oceantechnics and Marine Technology St.-Petersburg State Marine Technical University, St.-Petersburg, RUSSIA Finland, Kemi March 4-6, 05

For maintenance of navigation during wintertime in Arctic seas, icebreakers create the wide channels in the fast ice cover or pack ice cover at water areas near to ports with intensive traffic of

2 For maintenance of navigation during wintertime in Arctic seas, icebreakers create the wide channels in the fast ice cover or pack ice cover at water areas near to ports with intensive traffic of vessels. At present similar method is applied to provide winter navigation in the Baltic Sea. Within such wide channels cargo ships and tankers can move in both directions independently without icebreaker pilotage among small ice floes. Small ice floes fill the channel and their sizes depend on thickness of ice cover and their number (concentration) depends on the age of channel that is number of running of icebreakers and ships. Because the cross sectional dimension of channel is restricted the ships are forced to produce overtaking or opposite motion on close distance between their boards. As result the side force and yawing moment arise on their hulls that are able to cause the collision with other ship or edge of channel. Because the space between ship hulls is filled by small ice floes, the interaction between ships differs from one at open water surface (without ice cover). Theoretical studies of stated problem were organized after special experiments in Ice Basin of Krylov Research Centre on project MS GOF and implemented mainly under projects RescOp and WINOI. This presentation contents the improved analytical model of interaction of ship under navigation among small ice floes and results of computer simulation of their interaction when opposite motion.

Under navigation of the ships among small ice floes their ice resistance (except for dimensions and speed) depends on the thickness of ice, sizes of ice floes and its

When opposite navigation the ships appear nearby and distance between their hulls decreases quickly.

3 Under navigation of the ships among small ice floes their ice resistance (except for dimensions and speed) depends on the thickness of ice, sizes of ice floes and its concentration s 0. Ice concentration on ambient water area is constant and increases only near boards of ship when hull pushes aside ice floes that its bow part meets. When opposite navigation the ships appear nearby and distance between their hulls decreases quickly. Ship hulls move ice floes into space between them and the ice concentration increases from initial value s 0 up to value s. Therefore the ice concentration on inner boards of ships s exceeds the outboard ice concentration s 0 all time, when ships hulls overlap one another. s s. 0

4 a. Initial ice concentration around ship hull: s = item = s 0. Process of the ice concentration variation b. Shearing of ice floes by boards of ships in space between them and increasing of ice concentration between hulls: s > s 0. c. Ice concentration between ship hulls achieves limiting value s = 0. Future increasing of ice concentration is impossible. d. Distance between ship hulls decreases, shearing of ice floes continues. Therefore rotation and submerge of ice floes occurs. Effective thickness of ice cover increases: h > h 0.

Forces the ship hull effects on ice floes.

5 Forces the ship hull effects on ice floes. oads from ice floes on the ship hull. P shearing of ice floes, P friction, P 3 submerging. R sb ice resistance on starboard, R lb item on port side, F s side force, M yw yawing moment. Simulation of opposite ships movement by means of narrowing of the ice channel. Effect of variation of ice concentration between ship hulls (a) is same as under navigation within ice channel with variable width (b).

6 The opposite moving ship is simulated by means of narrowing of the ice channel width during its passing. It means the distance between ship hulls d corresponds to the width of ice channel on starboard. Distances from hull to left border of channel ps and to right border sb before and after opposing ship are much more than distance between hulls d. d, d. sb ps The ice concentration s increases in inverse proportion to the beam distance between ships d in comparison with ice concentration between reverse board and edge of channel. Increase of ice concentration effects the increase of ice loads on ship hull that results in initiation of additional ice resistance R, side force F and yawing moment M during passing. The speed of ship at issue is equal to sum of both ships speed (V +V ). Developed conceptual model allowed to parameterize the additional ice resistance R, side force F and yawing moment M that arise under interaction of vessels within ice channel by the difference of ice loads on left and right boards of ship at issue.

7 Second step is application of method to calculate the ice resistance of vessel that navigates in the broken ice floes field developed Kashtelian (et al, 980), that is formula: B Ice Ice Ice Ice ID Ice Ice Ice ID 0 R 0 b h k f k b h B f tg Fr B k b h tg Fr. 3 Ice Ice Ice 0 R Ice - ice resistance of the broken ice (without water resistance); b Ice average size of ice floes; h Ice average thickness of ice floes; Ice density of ice; f ID ice friction factor against hull plating; - length and B width of the ship; - waterline area coefficient; E angel between tangent to waterline at bow and centre line; Fr Froude number; k, k, k 3 empiric coefficients depending on ice concentration s. Average dimension of ice floes b Ice h Ice is relatively constant (data during trial observations), and within ice channel made by ice-breaker the value b Ice h Ice depends on ice (pack or fast) cover thickness h Ice : b Ice 0.54h Ice

8 oads caused by deformation of ice cover at moving apart ice floes by ship hull and their friction on hull plating produce main contribution to ice resistance of each ship board. First item in Kashtelian s formula defines these loads on whole ship, when ice concentration is same on both boards. Scheme of the ice forces effect on element of a waterline in point A: - N load from moving apart ice floes, - S - a friction of ice floes on plating - y(x) co-ordinate of waterline. Resultant affect of ice loads in projections to axes of co-ordinates: - dr elementary ice resistance - df elementary side force, and - dm elementary yawing moment.

9 Projections of effecting on an element of waterline first group loads on coordinate axis determine: - elementary additional ice resistance - elementary side force - and elementary yawing moment dr k x b h y x k y x dx Ice Ice Ice fr, df k x Ice bice hice y x kfr y x dx, Ice Ice Ice dm xdf y x dr k x b h y x x y x dx. Empirical coefficient k based on model and full scale experiments is function of ice concentration s and relative width of ice channel m for starboard (right board): k s s, m 0.s s 0.0s m.05. For portside (left board) relative width of ice channel is enough large and it is possible to neglect its effect on value coefficient k, that is 3.3 k s s 0.0s if s 6.75, p k p 0 otherwise.

10 To submerge ice floes that are superfluous ones (not located between hulls) following force is necessary per unit of length of waterline: df 0. h d s 0 d. s w Ice Ice In this formula w is water density, d is distance between ship hulls. h Ice is additional thickness of ice cover when superfluous ice floes were submerged between ship hulls. These second loads effect only on bow part of ship hull because on dead flat and stern the submerging of ice floes do not occur. It is necessary to take into account also additional friction of submerged ice floes. Projections of effecting on an element of waterline these load on coordinate axis determine: elementary additional ice resistance, side force and yawing moment as following w Ice hice d dr kk fr Ice bice hice yx dx, y x y x df w Ice hice d dx, y x dm dr y x df x.

11 Kinematic schema of opposing navigation under review ship and opposite moving ship : initial stage a and termination stage b. Coordinate system xoy is connected with bow of ship and directed on starboard. Coordinate system ξo is connected with bow of opposite moving ship and directed on its starboard. y (x) coordinates of ship waterline, y (x') coordinates of ship waterline in connected with ship system. Ice concentration between hulls Relative width of canal s tx d s d y x y Vt x 0, 0, 0 Bc x d0 yx, mt, x d0 y Vtx. B

12 The first group of Ice loads: additional ice resistance R S, side force F S and yawing moment M S, on the first stage of opposite movement: (t). t R t b h k t, x k y x k y x dx, s Ice Ice Ice 0 fr 0 t t F () t b h k x k y x k y x dx, s Ice Ice Ice 0 fr 0 M t b h k t, x k y x x y x dx. s Ice Ice Ice 0 0 The second stage of opposite movement: (t). t t t R t b h k t, x k y x k y x dx, s Ice Ice Ice 0 fr F () t b h k x k y x k y x dx, s Ice Ice Ice 0 fr M t b h k t, x k y x x y x dx. s Ice Ice Ice 0

13 The second group of Ice loads (submerging ice floes in the bow part of hull) produces following values of additional ice resistance R S, side force F S and yawing moment M S f f hice(, t x) d t, x dx Rs t kfr Ice bice hice kt, x yxdxw Ice, x s xs y ( x) F f hice(, t x) d t, x y ( x) dx s() t wice, x s y ( x) f, M t k b h k t x y x dx s fr Ice Ice Ice w Ice x s w Ice f x s f h Ice hice(, t x) d t, x y ( x) xdx. y ( x) x s (, t x) d t, x y y ( x) x dx In these formulas x s is distance where s = 0, x s - f is length of bow part of hull.

14 Total loads that arise on the hull of under review ship when opposite moving ship drives near it are defined by summarizing of both examined groups of ice loads: shearing ice floes and friction along boards (R s, F s, M s ) and also submerging of non located between hulls ice floes (R s, F s, M s ):,, R t R t R t s s s F t F t F t s s s M t M t M t s s s Time duration of interaction of opposite moving ships is determines by their common length and sum of their velocities:. T f V V. Under computations following norming was applied: - for forces - for moment c c c R F M w w w V V V R s F s B B M s B,,.

15 Equations for waterline y (x) of the under review ship ( f length of dead flat, 0/ and 0/ angles of waterline slope on 0 and 0 frames): yx 0.5 B 0. 5 x f tg f f f 0 / if 0 x 0.5, f y x 0.5 B if 0.5 x 0.5, f tg 0/ B x yx 0.5 B if 0.5 f x f B Form for waterline of under review ship -y (x) and angles of its slope = arctg[y (x)]

16 Equations for waterline y (x) of opposite moving ship in system coordinates xoy connected with the under review ship : ( f length of dead flat, 0/ and 0/ angles of waterline slope on 0 and 0 frames): f tg0/ B Vtx f 0.5 f y x 0.5B if Vt x x 0.5, f f y x 0.5B if 0.5 Vt x 0.5, f tg0/ B Vtx yx0.5b if 0.5f 0.5 f Vtx.

17 Computer modeling of ships interaction during passing among small ice floes within navigable ice channel Input data (basic version):. Under review ship : = 0 m, B = 0 m, V = 5 m/s.. Opposite moving ship : = 0 m, B =0m, V = 5 m/s. 3. Velocity of passing: V = 0 m/s. 4. Ice thickness: h 0 = 0.5 m, ice concentration s 0 = 7 balls. 5. Minimal traverse distance between board of ships: d = 0 m. Variation of input data:. Distance between boards: 4 m < d < 50 m.. Ice thickness: 0.05 m < h 0 <.0 m. 3. Ice concentration: < s 0 < 8 balls. 4. ength of opposite moving ship : 60 m < < 300 m.

18 Variation of additional resistance C R, side force C F and yawing moment C M on the hull of under review ship during passing with opposite moving ship. Inputted data: = 0 m, B = 0 m, V = 5 m/s; = 0 m, B = 0 m, V = 5 m/s; d = 0 m. Ice thickness: h 0 = 0.5 m, ice concentration s 0 = 7 balls. C F < 0, it means side force F s effects in opposite direction on passing ship, C M > 0, it means yawing moment M effects on bow to passing ship direction.

Ice resistance of ship when self-supporting navigation under ice thickness h Ice = 0.5 m and concentration s 0 = 7 balls is R ms = 49.6 kn (coefficient of ice resistance c R = 0.04).

19 Ice resistance of ship when self-supporting navigation under ice thickness h Ice = 0.5 m and concentration s 0 = 7 balls is R ms = 49.6 kn (coefficient of ice resistance c R = 0.04). Maximal values of additional ice loads when passing with opposing ship are following: - ice resistance R s =.9 kn (c R = ), - side force F s = 735 kn (c F = 0.05); - yawing moment M yw = knm (c M = 0.06). Additional ice loads have significant values. As result, it is possible collisions by bow with opposing ship or by stern with channel border.

20 Dependence of ice loads on minimal traverse distance between board of ships for ice thickness h Ice = 0.5 m and concentration s 0 = 7 balls. Ice loads increase intensive as distance between ship hulls decreases. eases.

21 Dependence of ice loads on initial ice concentration s 0 for ice thickness h Ice = 0.5 m and distance between ship boards d = 0 m. Ice loads increase intensive as ice concentration increases.

22 Dependence of ice loads on initial the ice thickness h Ice for ice concentration s 0 = 7 balls and distance between ship boards d = 0 m. Ice loads increase intensive as ice thickness increases.

23 Dependence of ice loads on hull of under review ship upon dimensions of opposite moving ship for the ice thickness h Ice = 0.5 m, ice concentration s 0 = 7 balls and distance between ship boards d = 0 m. Side force increases considerably under passing when dimensions of opposite moving ship increases.

CONCUSION Developed mathematical model is closed one and gives possibility to calculate the side force and yawing moment affecting on ship hull during maneuvering with opposing ship under navigation

24 CONCUSION Developed mathematical model is closed one and gives possibility to calculate the side force and yawing moment affecting on ship hull during maneuvering with opposing ship under navigation among small ice floes within navigable ice channel and among broken pack ice. Model can be adapted for calculation of loads on both ships that affect at one time while opposing. Model of interaction of ships is suitable for small ice floes concentration up to s = 8 balls. It is possible to apply developed model for evaluation of safe distance between ships as function of their dimensions, velocities, thickness of ice and ice concentration. Model can be applied to create special programs for simulators for training navigators to safe maneuvering while traffic within navigable ice channel and opposite navigation in broken pack ice.

25 Studies were implemented within Projects: RescOp The Development of the Rescue Operation in the Gulf of Finland, WINOI Winter Navigation Risk and Oil Contingency Plan. Projects are co-funded by the European Union, the Russian Federation and the Republic of Finland. Thank you very much for your attention

Interaction of Ships within Navigable Ice Channel

RescOp - Development of rescue operations in the Gulf of Finland International Seminar: MARITIME SAFETY IN THE GULF OF FINLAND Interaction of Ships within Navigable Ice Channel Vadim K. Goncharov Department