But at 90 degree, if your speed is lower than 2 knot, it will be quite. Now, obviously, what happen at this is this angle is, let us say, is a, you know, 45 degree this line, now it’ll tell that.
But at 45 degree angle of heading, I can go up to 4 knots and at 90 degree, sorry, and at, this will probably straight out. In fact, normally it’ll go like that.
Now the angle, see you are plotting there, see you are actually finding the boundary points and then joining them together. You are actually, what you are doing, you see, you have again, if I do that, you have a diagram. Here, you have actually calculated for every v and every mu, and then you find out which v and mu combination it is, just having the threshold value.
So, this boundary of this curve, you find out by some rough, it can be rough interpolation. You see, for example, you found out, let let me give an example. See, you have done a calculation for 45 degree and for say, 90 degree you find out that at 45 degree, you know like my slamming is so and so, 90 degree slamming is less.
So, you kind of interpolate, see, let us say my slamming should not be, and not occurred more than say 30 percent.
Now, you find out that at 0 degree heading angle, my slamming does not occur, but at thirty degree heading angle say, at some heading angle here, my slamming occurs 50 percent at 10 percent time.
At these, it occurs say 40 percent time. So, you can interpolate and find out thirty percent time will occur at what what heading angle.
It is some kind of an approximation as far as interpolation is concerned. See, please understand this way. Other way round, I will show you another another graph. See, you have a got a slamming here, some slamming with respect to say v.
So, this graph goes like that. As the speed goes up, slamming also goes; it goes like that, now your slamming criteria is this.
So, you’ll tell that my if my speed is this, is for a mu equal to some degree say, some say, 45 degree.
So, you’ll say at 45 degree, if my speed exceeds this much, then my slamming is going to be more than that acceptable limit.
Similarly, now you do that for another angle. Like that, for each angle, you find out what is my threshold velocity or the other way round. Therefore, in this diagram, for each angle, see, this is my angle, I will find out up to what velocity I can go without slamming.
Here, I will find out, say, here I found out this next angle. I find that up to, I will say that this line here, I find out this is this line.
So, I join this, then I know that I cannot go on that. Another diagram is necessary, see, you let us see from this diagram only.
(Refer Slide Time: 43:35)
So, what I did is that, simpler case, we shall take, where as velocities diagram are there. Let us say this is like that. Now, I find out that at this angle, at this particular heading, I
can go up to all the speeds. No slamming at this angle. I can go up to this much speed beyond that, it is going to slam.
At this angle, I will find out that I have to go up to only this speed; beyond that it slams at this angle, I can go only up to this speed. So,.
That means, I must be below this zone. So, similarly, I finish this side. So, what it happen is that, if I am in this zone of operation, if this zone of operation, then it is going to slam more than what I prescribed.
So, my slamming must be lower than that. that Now, I know that this is my area where I can operate without the slamming. So, this was slamming.
Now, you do for that for all. So, actually you can do in a same diagram all this area. So, now, this is for slamming.
Now, you find out that pitching, pitching (( )) for for pitching, because pitching normally will be more here. You cannot operate if it is with this range. Let us see.
For another Response, you may find out you cannot operate within this range. Now, you over lap all of them, then, you will, whatever is remaining area, you you can tell that the remaining part I can operate which satisfies all the criteria. This is what is called operability criteria.
See, if you have given a set of criteria a b c d 10, you find out a is possible. It is this combination b is possible, this is the combination c is possible. Then you add them up; you can tell that in sea state 3 I can operate up to, you know, in this speed and this heading.
Why this is important because, if you have that and if you had a bad motion experience, you can actually from there estimate and try to change your speed and heading angle.
This is why you have operability. See, if you have a roll operability index, you know that you are suddenly meeting very high waves and very this thing.
So, you can approximately estimate which you know what kind of angle and speed I should reduce in order to eliminate. That you do by experience, but this helps as a guide.
From the design point of view, you can actually find out by the percentage area. See, the remaining area. If you have done all that you know area area etcetera, whatever is remaining, this as a percentage of the full area will tell you what the percentage of the operability area that you can operate.
In a given sea state, obviously, what will happen? This is going to be actually become less and less as the sea state goes up. Because you have to do that for all sea states, see if, see for example, sea state 3, you find out this is my non operation area. In a higher sea state, you may find that this you cannot operate, you know.
Obviously, as the sea becomes rougher, you you your operability goes up, you can then, there is no end to it. You can further combine now, you know, that in sea state 3, I can operate in this combination 4, I can operate this 5.
Now, sea state 3 means h is equal to 3 meter 4 means h is equal to 4. Now you combine, you find out that in in in a long term 3 meter height occurs only 10 percent time.
So, this into point 1 4 meter occurs 20 percent time this into point. So, you can again combine that 2 with a long term weather statistics
So, there is a lot of statistics you can generate. You can make lot of graphs, but essentially statistics means just finding out percentage of occurrence of certain ships motions within certain, you know, like percentage of operations of certain motions or Derived Responses in a given sea state and combining them in some fashion. This is more of an algebraic operation if you keep your minds straight within, with common sense you can work it out.
What you cannot work out, is finding out the Response itself. That requires mathematics and some hydrodynamics.
But if you have the Response found out by some means, you know that you know 10 degree or 5 degree, to tell that you know, like the limits. That is a more of a common sense, you know, you know 10 degree occurs at 90 degree heading angle at 20 knots speed.
But, if you make it fifteen knot speed, the angle will come down to 60. So, you can make it out from there, it is very common sense. See, somebody says that, look, I cannot allow the ship to roll more than 8 degrees, then you find out that 8 degree would occur when the ship speed is 16 knots, but if you go more than that, it becomes more. (( ))
So, you know you know like by your experience. So, basically this polar plot, that v 2 is a plot that you have just to synthesize. You may say what you have done, if I if I tell another thing.
(Refer Slide Time: 48:24)
See, you have got various weathers, that are sea states. You have got number of weather a number of weather conditions, you have got number of combinations of speed and heading angle, speed and heading. For all this, you have got ship ship motions.
For all this, you have got Derived Responses and for all this you have got the statistical information; that that is, you know how much percentage (( ))
So, you all (( )) combining all the 2. So, it is a lot of repetitive calculation, repetition for each sea state. For all combinations, you find all the ship motions and all the Derived Response and all what you require by statistical analysis that you know, you repeat that. You have got a large chunk of information.
Then you just put them together in various forms; that is all we are doing here. So, you know this part is a post processing part; it is actually playing with large numbers.
Lot of people have window based programs nowadays. You know where you can do that, but as I said, to find out ship motion, the most complicated part actually still arises here, in fine motion, in regular waves that is, or RAO. This is the most demanding task from evaluation point of view, but from practical point of view, you would like to see this results.
But, if you have that, my point is finally, is that, if you have that. To get this part may appear to a beginner complicated, but really it is not complicated. It is a tedious, long calculation.
But not very complicated if you keep your mind you know focused, that is all. Sea keeping is viewed to be complicated subject, but what the part of sea keeping you view as complicated is actually the simpler part. I mean with that, I will end my lecture today and we will formally close the ship motion in waves part of the lectures. Thank you. Polar plot you.