(Refer Slide Time: 06:48)
I just want to say very quickly, 1 of them you can call Bow Motion. What is Bow Motion? it is actually, this is a ship here, you take a bow point say, f p what is the vertical motion in f p? Fine, that is no problem. You can just find out vertical motion by combining given pitch. You know, all you are doing is that you what is the motion? what is my z motion at bow, means, what is my z motion at x equal to say L by 2 or whatever something like that or at x equal to f p?
This is my Bow Motion. You understand why why people want to know Bow Motion. Because, you want to know how much bow is going. But, that is not the important thing. What people want to know is relative Bow Motion. That is, if there is a wave here, there is a there is a wave here.
Now, you would know, I will know, my Bow Motion z at bow. This will be given by sub formula say something into Cos omega t plus some phase angle, something like that, I will get that by combining.
Now, relative Bow Motion relative Bow Motion is going to be z bow minus the wave height at the bow minus say zeta at bow that I know what is zeta at bow. Because what is zeta at bow is nothing but it is zeta a into Cos k x minus omega t with take an x as L by 2.
So, you see the principle is very simple. principle is very simple Here, the ship has moved so much up and there, the you know the wave has moved so much up. So, you can find out how much the, you know, the relatively this point a given. Actually, here you have to take a particular point z bow. Instead of z bow here, you take a point here. Say, I will take a point p here.
Then, I can find out a point on (( )) on the 4 4 peak. For example, how how much it is from, with respect to wave; see, something like this.
(Refer Slide Time: 08:58)
I can tell at any point of time, this point, how far it is from this, because it can be next instance and you see the phase information becomes very important. Because, supposing, they this diagram is interesting, supposing I, my wave is here one case, let me use other color. So, I can have a wave going like that or I can have a wave here, at the, my this thing is very short or I can have the wave actually going like that. Then, I have got very high.
So, you see, what this of course, depends on the phase. when the see Just think of it when the wave is rising, ship might be going down. Then, my basically what happens is that that the relative Bow Motion will may come down to very small value or may become a very large value. So, it will oscillate between small to large value.
Now, what happens is that, here comes the interesting part. Now know this value, say r. Now, what I will do? I will find out, you see, at any point of time this r is becoming less than the free boat. See, after all, there is a free boat here, ok?
If r become less than the free boat, then I say that if r is less than say free boat in some sense, then I say that take (( )) occurred is it not?. Because, what happens that, you see, that there is so much gap.
Now, the wave has gone up, the ship has come down. So, the gap between that the the the height of the point with respect to wave height is suppose to be actually some number, but it has become less than some threshold number.
We can work the details, but the principle is very simple. There is a particular point, it is actually with respect to absolute value; so much height. So, with respect to wave it is so much height, but it must always be above the wave height.
So, you can find out if it becomes 0, if supposing this height, if I call this r, if this r has become negative. Actually, here, this is not same as minus free boat that is again using another reference; but just think if this point with respect to the wave.
I am I am I am saying that the distance of this point above the wave height, above the actual water surface, this r that is relative motion of this point.
In fact, they call the relative motion of the point, actually at this location. That is why this free boat comes in. But forget it, just think the concept. I take a particular point as a representative point, I will say that if that point comes down below water, then it is the deck is getting wet. Let us draw this another picture in a better way.
(Refer Slide Time: 11:43)
So, I have a point here, let me see, a I just draw this
(( ))
Yeah, if I take this point actually, now supposing, I have this point, and this is my wave height and this is my reference. See, some reference is like this is my reference. Now what happens, see here, you can say free body, mean water line, whatever some this thing.
Say this one is my Bow Motion, how much is going, and this one is my wave height and this much is my relative motion, and you are doing negatively in this case. You see that r which, if I take this, see supposing I call this to be Bow Motion p and if I call this to be zeta b minus zeta and this is becomes negative.
You know in other words zeta has become more than b. So, therefore, the take is weight. So, I can find out. from the again Since I have got now, what I will do is that I will take for this r a spectrum, because you see this r is nothing, but again a sine motion.
So, I can find out see r. If you expand, that r will turn out to be equal to some amplitude into some Cos omega t plus beta, something like that.
So, I can find out basically RAO, for you know RAO for relative Bow Motion and I can draw a spectrum.
Then, I can, from a spectrum find out what is the probability of my r becoming less than 0. You see, I (( )) the spectrum, know I know the value of s etcetera and as I told you that from there you can find out all quantities of this Response whether it is less than. So, and. So, what is the chance it will be more than. So, and so.
What How many times it’ll occur once in so many years, all that you can find out. So, you see very simple, I mean formulas, I am not going to the formulas, but the principle is important. You can find out very easily just by another 1 line formula, what is the chance or what is the probability or what percentage percentage of time r becomes negative.
So, you can tell suppose it is 25 percent of time in that particular sea state r becomes negative.
So, you say that (( )) 20 percent of time people actually say in terms of cycles the you know that can be that can be said that how much at every how many seconds r will become negative
So, you say, let us say that is 5 seconds. So, you will see that every 5 second I have got a deck getting wet every 5 second the deck is wet like that all information that you want statistically you can find out from there for this
So, again you see this is the Derived Response because how did I get r r is nothing, but Bow Motion minus of wave motion which all are available to me and again as I mentioned before it is again a sinusoidal wave motion
Now, exactly same way, I can find the step of probability of slamming. What is slamming? The other way round, slamming would be, in in in a case of slamming, it would be, I do not say slamming right now, let us say it is the probability of bow coming out of water. Again, you take this point or some point and find out again. It is you know, relative motion the other way round, if you take this point for example.
If this point is above this height then, obviously, it is the deck has come out the fore peak, has come, you may call fore peak emergence, fore peak has come out.