Weight Distribution Calculations in ShipWeight

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Weight Distribution Calculations in ShipWeight

Additional Features > Weight Distribution

The following attempts to describe how weight distribution is calculated in ShipWeight.  In general, ShipWeight approximates the distribution for each individual weight item to either a uniform, triangular or trapezoid distribution.  These individual items are then added together making up the total “accurate” distribution.  The accurate distribution can be converted to a distribution of stations or bars.

Consider the following weight items:

Nr

Weight

LCG

LCG_min

LCG_max

1

10000

50

0

100

2

6000

40

20

60

3

2000

30

10

40

4

2000

58

50

70

 

In ShipWeight, the distribution of these items will individually be represented like this:

1. Item with uniform distribution:

image56_168

 

2.Item with uniform distribution:

 

image56_169

 

3.Item with triangle distribution – LCG located at 2/3 of the items extension

 

image56_170

 

4.Item with trapezoid distribution – LCG between 1/3 and 1/2 of the items extension

 

image56_171

 

When ShipWeight calculates its “accurate” distribution, the items are added together.  Compare the colors in the individual representations with the colors of the “accurate” representation to locate each weights item’s contribution to the total curve.

 

image56_172

 

The user may choose to represent this curve in stations. ShipWeight calculates the stations by dividing the “accurate” curve into the number of stations to be plotted.  Each share of the “accurate” curve is integrated giving the area under the curve between the stations.  Next this area will be represented by a station or bar with the same area as the curve area it replaces.

This secures a one to one relationship in area between the “accurate” curve and the station curve. Further, this means that the area contribution from individual items which distribution is covering more than one station will be split into appropriate parts in each station. This secures the best possible conversion between “accurate” and station curve.

See figure on next page representing the station version of the curve. Again, the colors will help compare the curves to visually inspect how conversion takes place.

 

image56_173

 

In both cases, the area under the distribution curve equals 20 tons. The figure below shows the “accurate” curve drawn in red with the station curve superimposed and drawn in green. This shows how the curve is transformed and the area preserved.

 

image56_174

 

Of course, the same reasoning is also valid with any other number of stations, not just 10. The figures below shows same principles for the distribution curves as discussed above, only this time with a 20 station curve.

 

image56_175