ROTI

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What is ROTI (Rate Of Turn Indicator )?

 RATE OF TURN INDICATOR (R.O.T.I.) Unlike road vehicles a ship does not turn sharply. With lesser friction in water and under the influence of momentum a vessel continues on her initial course for some time, begin ning to turn slowly and then rapidly later. Vessel thus traverses a curved track which can be treated as an arc of  a circle. For small ships such arcs are small and can be executed without much problem. But for large sized merchant vessels these arcs assume greater radii and need to be treated differently. This becomes all the more important when vessel is altering courses in restricted waters or in close proximity to navigational hazards. For same reasons roundabouts are charted in traffic separation schemes. Under navigation watch keeping principles, vessel is required to do berth to berth passage planning. It is also required to lay courses in curved segments as well, where required and to mark  the wheel over positions. In view of the above, vessels having 50,000 GT and above are mandatorily required to be fitted with ROTI (Rate Of Turn Indicator) as per Chapter V, SOLAS. ROTI assists OOW in planning, executing and monitoring vessel’s progress along curved segment of charted course.

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What is ROTI (Rate Of Turn Indicator )?

The purpose of ROTI is to provide rate of turn to port and to starboard side of ship. The indicator is usually in the form of a circular dial with zero at top. Port turn is indicated on left of zero and starboard turn on right of zero. Graduations are provided to indicate ROT up to at least 30 degrees/minute on either side. ROTI can be self-contained, or it may derive information from other equipment or it may form a part of the other equipment. However, the design is such as to preclude degradation of other equipment to which ROTI is connected, irrespective of weather ROTI is in operation or not.

 DERIVATION OF FORMULA F ORMULA FOR ROT: ROT: ROT ( /t) is expressed in degrees per minute. Consider following diagram: PB = Initial course BN = Final course AC = Curved segment of charted course; A is commencement of turn and C is completion of turn. Length of the curved segment = d  = Amount of alteration in degrees (Angle MBN or Angle AOC) C  =  in radians R = Radius of the circle of which arc forms the part t = Time

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What is ROTI (Rate Of Turn Indicator )?

Now, we know that, by definition, radian is the angle subtended at the center of a circle by an arc equal in length to the radius of the circle. Thus, we have: C  = d/R = (V x t)/R o

Or,  /57.3 = (V x t)/R (Note:



is in degrees)

Or,  /t = (V x 57.3)/R in degrees /hour Or,  /t = (V x 57.3)/60R in degrees degrees /minute Using approximation and cancelling 60 and 57.3 with ea ch other, we have:  /t

= V/R in degrees /minute

Thus, we have ROT (  /t) given by:

=V t R

(degrees per minute)

EXAMPLE: Let us assume that a vessel’s initial init ial course is 000 (T) and final course is 060 (T). She is steaming at 15 knots and intends to negotiate a turn about an islet keeping a distance of 1.5 miles. What will be the ROT and a nd how long will she take to complete the turn?

=V t R

(degrees per minute)

So, ROT = V/R = 15 / 1.5 1. 5 = 10 degrees. Thus vessel will turn at the rate 10 degrees per minute, while maintaining a distance of 1.5 miles from the islet. Now amount of alteration = 60 derees Thus vessel will take 60/10 = 6 minutes to complete the turn

CONSTANT RADIUS TURN: In this method radius R is kept constant. We have seen that rate ra te of turn (ROT) is given by (  /t) = V/R Or, R = V/ (  /t) If radius R is to be kept constant, the expression on the RHS will have to be kept constant. But as vessel turns, velocity V reduces. Thus ROT (  /t) will have ha ve to be varied proportionately so as keep R as constant. Thus in  constant radius turn ROT does not remain same and changes as vessel

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What is ROTI (Rate Of Turn Indicator )?

negotiates the turn. Constant radius turn is negotiated in the following two ways, depending on weather the object ‘O’ is visible or imaginary.  Object ‘O’ available as visually or radar conspicuous feature: 1. With O as center and R as radius draw an arc. (The value of R will be decided by OOW/Master and will depend on vessel’s size, draft, weather conditions, proximity to other dangers etc,). 2. Draw AB and BC as tangents to the arc, representing repre senting initial and final courses  Object ‘O’ not available as visually or radar conspicuous feature:

1. Draw initial and final courses first. 2. Choose suitable value of R depending on size, loading condition of vessel, weather conditions etc. 3. Calculate AB = BC = R tan  /2 4. Draw small arcs, with radius R, from A and C to cut at O. 5. Now O as center and R as radius, draw arc AC. This is the curved segment of the planned course.

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What is ROTI (Rate Of Turn Indicator )?

 MONITORING THE TRACK ALONG CURVED SEGMENT: SE GMENT: 

Object O is visually conspicuous:

We know that any radius to the point of contact of a tangent is perpendicular to the tangent. This means that for vessel to remain on the curved track, the object O must remain abeam or very nearly abeam. If the object is falling abaft the beam, it means that vessel is going outside the arc (or she is turning slowly) and ROT needs to be increased by giving greater helm. Conversely, if object is moving ahead of beam, vessel is going inside the arc (or she is turning too fast) and ROT needs to reduced by easing the helm.



Object O is radar conspicuous: In this case VRM along with parallel indexing techniques is utilized for keeping the vessel on the curved segment of the track. Both RM and TM modes are equally suitable for the procedure.

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What is ROTI (Rate Of Turn Indicator )?



Object O is imaginary: In this case vessel’s position has to be closely monitored at more frequent intervals to ensure that the vessel stays at the curved segment of the track.



With ECDIS onboard: ECDIS has brought a revolutionary change in the way we navigate navigate ships. ships. The way computers have made many old human skills irrelevant; ECDIS is also likely to play the same role. As per IMO performance standards for “route planning and monitoring” m onitoring” on ECDIS, it should be possible to draw both straight and curved segments of planned courses. Thus, executing and monitoring ship’s progress along any curved segment is very easy. The fact that the courses drawn can be seen against the background of chart on the screen itself  makes the procedure a very simple task. ECDIS provides real time fixing. Hence, OOW knows where the vessel is at any moment rather than where she was few moments ago.

CONSTANT RATE TURN: In this method ROT (  /t) is kept constant. We know that rate of turn (ROT) is given by (  /t) = V/R If ROT is required to be kept constant, the expression on the RHS will have to be kept constant. But as vessel turns, velocity V reduces. Thus radius R will have to be varied proportionately so as to keep ROT as constant. Thus in constant in constant rate turn radius R does not remain same and changes c hanges as vessel negotiates the turn. Practically ROT is calculated for a mean value of vessel’s speed (mean of speed at the start of  curved segment and speed at the end of curved segment). This value corresponds nearly to vessel’s position midway on the arc. At other locations on arc value of radius will differ from R. But these variations are small and within practical and tolerable limits.

WHEEL OVER POINT (WOP): It is the point on initial course at which wheel is put over to initiate the turning of the vessel. It is obtained by intersection of initial course by wheel over line. The distance between the WOP and the ship commencing its turn is denoted by F and depends on:  Size of vessel  Loaded/ballast condition  Trim  Type of vessel etc.

WHEEL OVER LINE: It is a line drawn parallel to the final course. The point at which it cuts the initial course line is the wheel over point. The distance at which wheel over line is to be drawn parallel to the final course is given by following formula: F Sin + R (1 - Cos)

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What is ROTI (Rate Of Turn Indicator )?

F= distance between WOP and a nd the point when vessel begins to turn. R= radius of turn  = difference between initial and final course

 PROCEDURE: 1. Take F as 0.1, 0.15 or 0.2 miles depending on weather vessel is small, medium or large in size. 2. Take R as radius of turn, depending on your vessel’s size, draft and external factors. 3. Calculate the distance between WOL and final course by the formula given above. abo ve. 4. Take any arbitrary point on final course and draw on arc, towards initial course, at the distance calculated. 5. Draw a tangent to the arc parallel to the final course, cutting the initial course. 6. The point of intersection is the wheel over point.

 For illustration purpose only

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What is ROTI (Rate Of Turn Indicator )?

 EXAMPLE 1: A small vessel is coming out of Aberdeen harbour at a course of 056 (T). Her next course is 120 (T). With the Racon Girdle Ness as centre and 0.52 miles as radius, find the WOP. If the vessel is steaming at 10.4 knots, find the rate of turn and time taken to complete the turn.

SOLUTION: !Distance between final course and a nd WOL is given by: F Sin + R (1 - Cos) Substituting the values, we have: 0.1Sin 64 + 0.52 (1- Cos 64) = 0.38 miles. Now, take any arbitrary point on final course and draw an arc at a distance of  0.38 miles. (Refer to the photo above). Draw a tangent to the arc parallel to the final course to cut the initial course at T. Now, the parallel line drawn is the wheel over line and T is the wheel over point. Now,

=V t R

(degrees per minute)

Thus, rate of turn = 10.4/0.52 = 20 degrees/minute Time taken to complete the turn = 64/20 = 3.2 minutes.

 EXAMPLE 2: A small vessel is leaving Aberdeen harbour and is steaming a course of 056 (T) at a speed of 13 knots. Her next course is going to be 190 (T). Draw the courses with curved segment using the Racon Girdle Ness as centre and 0.52 miles as radius. Also, show the WOP. How long will she take to arrive at the point of final course?

SOLUTION: Distance between final course and a nd WOL is given by: F Sin + R (1 - Cos) Substituting the values, we have: 0.1Sin 134 + 0.52 (1- Cos 134) = 0.95 miles. Now, take any arbitrary point on final course and draw an arc at a distance of 0.95 miles. (Refer to the photo below). Draw a tangent to the arc parallel to the final course to cut the initial course at T. Now, the parallel line drawn is the wheel over line and T is the wheel over point. Now,

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=V t R

What is ROTI (Rate Of Turn Indicator )?

(degrees per minute)

Thus, rate of turn = 13.0/0.52 1 3.0/0.52 = 25 degrees/minute Time taken to complete the turn = 134/25 = 5.36 minutes.

 For illustration purpose only

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