Question regarding m-rad and m-degrees

Hey Guys,

I’m studying to further improve my skills and have come across a question I need a little help with.

I have to write a report on compliance against NSCV which is a stability code in Australia for commercial vessels.
I have a stability manual for a vessel including hydrostatic stables, and intact stability for various loaded conditions.
Obviously I’m going to compare the values at their worst (Fully loaded, for departure) when the boat is its heaviest/most loaded for criteria to comply.

I am stuck at a section of the criteria:

[I]All vessels within application, Clause 5.2

[/I]
[I]
The area under the righting lever curve between the angles of heel of 30 degrees and 40 degrees, or between 30 degrees and the angle of flooding [FONT=Times New Roman]θf if this angle is less than 40 degrees, shall be not less than 1.72 metre-degrees.

[/I][/FONT]

I do not know what “metre-degrees” is.
Same with m-rad i’m assuming meters-radians but I don’t know what this value means.
As far as I can see, I need to find out the righting lever curve area between 30-40 degrees, as the boat’s angle of flooding is more than 40 degrees, and it must not be less than 1.72metre-degrees.
In the stability manual it has values of area between them e.g
30 degrees heel to port = 0.4548 m-rad
40 degrees heel to port = 0.6294 m-rad

I was thinking along the lines of:
0.6294 - 0.4548 = 0.1746 m-rad
How do I convert this to m-degrees?

I am looking to learn how figure this out rather than just an answer on if it’s compliant.
Am I heading in the right direction? Do you need any further details to answer this?

If you look at a righting-arm diagram the x-axis is angle of heel and the y-axis is distance. The area under the curve is going to be the angle multiplied by distance. If the units are degrees and meters the units for area will be meter-degrees and if the angle units are radians then the answer will be in meter-radians. 360 degrees is equal to 2 pi (2x3.14) radians

1 Like

[QUOTE=Kennebec Captain;178741]If you look at a righting-arm diagram the x-axis is angle of heel and the y-axis is distance. The area under the curve is going to be the angle multiplied by distance. If the units are degrees and meters the units for area will be meter-degrees and if the angle units are radians then the answer will be in meter-radians. 360 degrees is equal to 2 pi (2x3.14) radians[/QUOTE]

Hi, Thanks for your input, can you verify if this is right?

The righting lever @ 40 degrees is 0.876M
and at 30 degree 1.119M

If I go
40 x 0.876M = 35.04
30 x 1.119M = 33.57

The area under the righting curve between 30-40degrees

35.04 - 33.57
=1.47M

This boat fails?
It’s a catamaran…

Thanks,
Aaron

[QUOTE=aaronjod;178845]Hi, Thanks for your input, can you verify if this is right?

The righting lever @ 40 degrees is 0.876M
and at 30 degree 1.119M

If I go
40 x 0.876M = 35.04
30 x 1.119M = 33.57

The area under the righting curve between 30-40degrees

35.04 - 33.57
=1.47M

This boat fails?
It’s a catamaran…

Thanks,
Aaron[/QUOTE]

Google " find area under curve"

The answer should be in meter-degrees. You can estimate the area using graph paper by drawing rectangles to approximate the area under the curve and then find the area of the rectangles (lxh). Adding the area of smaller rectangles will give you a better estimate.

Looks like 10 degrees (40-30) times 1 meter (average 1.1 and 0.9)= 10 degree-meters.

[QUOTE=aaronjod;178845]Hi, Thanks for your input, can you verify if this is right?

The righting lever @ 40 degrees is 0.876M
and at 30 degree 1.119M

If I go
40 x 0.876M = 35.04
30 x 1.119M = 33.57

The area under the righting curve between 30-40degrees

35.04 - 33.57
=1.47M

This boat fails?
It’s a catamaran…

Thanks,
Aaron[/QUOTE]

Dear Master,

It is the area under gz curve up to that mentioned angle . So basically we will need to use Simpson’s rule to find the area. Please note , if the gz curve is in meter vs degree, the area is in meter-degree.

Hope this is of some help.

Kind Regards,
Jok