So, you can more or less say k y y is approximately you know like 25 to say 30 percent of L this is a guess though one can always say why 25 why not 22 yes, but for you will find out the difference will not be. So, much in the prediction number one number two really you cannot hit the exact number whichever way you do it is an estimate. So, this is ok now comes to. So, what I am trying to get at this that I we want to make an estimate for real structure this value again it is at what period I have an excessive pitch. So, I need to estimate this and this for a real ship now let us look at I y y part the delta I y y part that added moment of inertia now once again here we we will look at this way. So, if I have this ship here take this section now if this section is this section now when this section is undergoing like the body is undergoing rotation this is try to come down the question is what is the kind of mass attach to it approximately if I take the same acceleration remember that that is a sectional added mass in heave that is the mass you would expect to be attached to this going down sectional added mass in this direction is what is the added mass of this contribution. So, if I take that m square the distance then add it up then I end up getting. So, called the added moment of inertia approximately once again now again you find out that that we have discussed last class a good estimate of that is that it is mass of the water of this surrounding semi circle. So, what it means is that this becomes again approximately the added moment of inertia of water mass having this you know like semi circular body just like the mass would be heave added mass would be mass of that pitch moment of inertia would be moment of inertia of that. In other words something like this if I were to draw in a different color as if this was the ship here and as if there is there is a another geometry you know like a kind of a geometry which is semi circular in look, but top is actually same breath mass of that becomes a approximately the added mass in heave moment of inertia of that becomes approximately the moment of inertia for pitch so; obviously, if you look at these again, you will end up finding that your delta I y y is, which I also can write k dash y y square into mass I can write in this fashion if want. This turns out to be all most equal to 0.25 in other words this is very comparable to I y y just like the other case we have found. So, therefore, if I were to write this you know I yy plus delta I y y delta what did
I write delta I y y. So, I can write this as I y y into one plus some factor say some c y y so this I can always call c y y to be you know like added moment of inertia divide by rigid body moment of inertia. So, this turns out to be again around 11.5 like that the factor just like what we have done before. So, this added moment of inertia plus moment of inertia which can be called virtual moment of inertia may be around two and half times rigid body moment of inertia approximately. So, you see the c y y of course, by definition is coefficient that is delta y y by I y y. So, this is around one to two may be lower may be higher in the order exactly same as what happen for heave added mass. So, we will
take this as bench mark for our estimates for you know like do it certain estimates