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14-Alexandrite

## Ship Stability and Graph Evaluation

Hello Community!

I'm working on a stability problem for a ship.

This involves the use of a GZ curve which I have successfully plotted with some help from Volker.

GZ in ship language is the righting arm i.e. GZ is a distance in meters and if multiplied by the displacement mass of the ship a righting moment is created.

In this problem a ship with the given GZ curve in my file has a mass moved from one side of the ship to another mass is 500 tonne and is moved a distance of 10m.

This creates a healing moment of w *d *cos(theta) where w is the weight of the object, d is the distance moved and theta is the angle of heel which the ship will be in after the object is moved.

The problem I need to solve is using the graph in my file work out which angles the ship will rest at i.e. moments be in equilibrium after the object of 500 tonne has been moved 10m along the deck of the ship (transversely)

I have approached this in the attached file by weighing out the moments as they must be equal for equilibrium to exist and have then tried to resolve/ simplify which I have come close to.

The issue I have now is I could evaluate the graph step by step to see which values would give equal values to my simplified formula but there must be a better way/ a simpler algebraic form of the two moments in equilibrium?

Andy

1 ACCEPTED SOLUTION

Accepted Solutions
13-Aquamarine
(To:awibroe)
Hi Andy,
if plotting the function Curve2 you need a varable: Curve2(Thetax)
regards, Volker
Volker
5 REPLIES 5
14-Alexandrite
(To:awibroe)

attached

14-Alexandrite
(To:awibroe)

So I have done some more reading and I need to plot a second line on my graph. The 2 points of intersection will give me the answer I need.

The line I need to plot is 0.5m*cos(theta) i.e. for every value of theta the plot needs to be cos(theta) *0.5.

I've tried experimenting in this regards but my knowledge of Mathcad's graphing is not good enough to know where I am going wrong.

14-Alexandrite
(To:awibroe)

The attached hopefully shows what I am trying to do i.e. a curve as a function of the x axis i.e. the each degree defined in the range but I am obviously not doing it correctly. Any ideas?

13-Aquamarine
(To:awibroe)
Hi Andy,
if plotting the function Curve2 you need a varable: Curve2(Thetax)