1、Section 4.2 - 4.3Righting Arm & Statical Stability Curves,A ship in static equilibrium is effected by outside forces that will alter its state of equilibrium.,G,MT,Wind,Water Resistance,The ship reacts to this external moment couple by pivoting about F, causing a shift in the center of buoyancy.,The
2、 center of buoyancy will shift because the submerged volume will change.,Note that there is no change in weight or its distribution so there is NO change in the location of G!,G,MT,Because the location of B changes, the location of where the FB is applied also changes. Because G does not move, the l
3、ocation of the Ds force does not change.,Ds,FB,G,MT,The external moment couple causes the creation of the internal moment couple to oppose it.,As a result, the ship is now back into equilibrium, even as it heels over due to the wind force.,We are concerned with the created internal moment caused by
4、the offsetting of the ships weight and the buoyant force.,Remember that a moment is created when a force acts at a distance from a given point.,The created moment is called the internal,RIGHTING MOMENT,This illustrates just one potential moment arm based upon one particular angle of f. There are an
5、infinite number of angles possible, therefore, an infinite number of moment arms that vary with the degree of heel, f.,If we can plot the heeling angle f versus the created moment arm GZ, we can create the Intact Statical Stability Curve.,This is a typical curve. Notice that it plots the angle of he
6、el on the x-axis and the righting arm on the y-axis.,The curve is in both the 1st and 4th quadrants (the 4th shows a heel to port). Typically only the curve showing a heel to starboard is shown as it is symmetrical.,The above chart plots the data presented in the text on p. 4-6 an 4-7.,With f at 0 d
7、egrees, the moment arm is also is 0. The buoyant force and the ships weight are aligned. No moment is created.,As the angle of heel increases, the moment arm also increases. At 25degrees, shown here, GZ is 2.5ft.,As the angle increases, the moment arm increases to a maximum here it is 4ft. As f incr
8、eases beyond this point the moment arm begins to decrease and the ship becomes in danger of capsizing,.Remember, the internal moment couple created here is in response to the external couple created by outside forces. At GZ max the ship is creating its maximum internal moment. If the external moment
9、 is greater than the internal moment, then the ship will continue to heel over until capsized.,The angle of heel continues to increase, but the moment arm GZ, and thus the internal moment couple, decreases.,The angle has now increased to the point that G and B are now aligned again, but not in a goo
10、d way. GZ is now at 0 and no internal moment couple is present. Beyond this point the ship is officially capsized, unable to right itself.,For any ship there exists the CROSS CURVES OF STABILITY. Like the Curves of Form, they are a series of curves presented on a common axis.The x-axis is the ships
11、displacement, Ds, in LTThe y-axis is the righting arm, GZ, in ftA series of curves are presented, each representing a different angle of heel f,By plotting the data from the Cross Curves of Stability for a given displacement, you can create an Intact Statical Stability Curve.,Example: Plot the Intac
12、t Statical Stability Curve for an FFG-7 displacing 5000LT,Step #1. From the Cross Curves of Form, find the 5000LT displacement value on the x-axis.,Step #2. Record the righting arm value for each curve, from f = 0 to 80 degrees,Intact Statical Stability Curve for FFG-7 Ds = 5000LT, But a correction
13、must still be made!,In the Cross Curves of Stability, the data is presented assuming that:,KG = 0 (on the keel),This is, of course, not realistic. It is done this way so that the curves may be generalized for all drafts.,Once the curve data is recorded and plotted, a sine correction factor must be applied,shifting the KG to its correct position in order to get the TRUE MOMENT RIGHTING ARM VALUE.,We will cover how to adjust the values within the table and the curve in the next section.,.To be continued.,
