9. Curves of Statical Stability

Question 1

What does Solas Require onboard all vessels with regards to Stability?

Answer 1

SOLAS requires that every vessel must be provided with stability information in a format and language readily understood by the officers. Note that the requirement is for “ship’s officers.”

Question 2

What is Dynamic Stability?

Answer 2

Dynamical stability is the measure of the work required to incline a vessel from the upright or the work needed to return a heeled vessel to her initial stable position.

Question 3

Explain a Radian?

Answer 3

A degree is a purely arbitrary measurement of 360° to a complete circle.
• A radian (57.3°) is a natural measure and mathematical constant
• Pi (symbol Π) = 3.142
• Π x 1 radian =180° (3.142 x 57.3 = 180°)
If the length of one radius is stretched around the circumference of any circle, an angle of 57.3° is produced.
This is one radian, which is the preferred unit of angular measurement for scientists and engineers as well as naval architects.

Question 4

16 Steps to Drawing your GZ Curve for the following vessel:

Initial GM 0.41m

Max GZ 0.42 @ 48°

Angle of Vanishing Stability @ 84°

Answer 4

Example

Initial GM 0.41m, Max GZ 0.42 @ 48°, Angle of Vanishing Stability @ 84°

1. Choose your paper – preferably squared or graph paper - and turn it to landscape orientation
2. Draw the horizontal axis 4 cm from the bottom edge along most of the page. Mark divisions 0° – 100° and extending on a bit further.
3. Draw the vertical axis 3 cm from the LH edge extending below the horizontal and going above the horizontal to a height that approx. equals the length of
   0° – 45° on the horizontal axis.
4. Of the information given in the question look at the Initial GM. If it is a negative number then that negative number is the start of your Vertical Scale. If it is a positive number then your negative scale starts at one
   division below zero. (The origin is still at zero on each scale even if the horizontal line is drawn in at a negative number on the vertical axis.)
5. Then take the higher number between Max GZ and Initial GM and that is the upper extent of your positive vertical axis. Mark and label divisions as appropriate on both the positive and negative parts of the vertical axis.
6. Label the Horizontal Axis “Angle of Heel (°)”
7. Label the Vertical Axis “Length of GZ Lever (m)”
8. Mark and label “1 Radian” at approx. 57° on the horizontal axis and draw a vertical line through this point.
9. Mark and label Initial GM (given in the question) on the vertical axis (I know this is the GZ Lever scale but ignore this confusing detail and mark it anyway!) and draw a horizontal line through that point.
10. Join the point where the 1 Radian Vertical Line meets the Initial GM Horizontal Line to the origin of the graph. The critical bit of this line is from the origin to about 15° Angle of Heel.
11. Remember that the point in Step 9 is only used to draw that critical bit of line from the origin. The point itself has nothing to do with the GZ Curve and may be on the curve, outside of the curve or inside of the curve. There is no connection between it and the curve!
12. Mark and label the Max GZ at the Angle of Heel it occurs.
13. Mark and label the Angle of Vanishing Stability on the horizontal axis.
14. Now draw the curve. You start at the origin and follow the Step 9 line to about 15° Angle of Heel. You should not go under this line and although it is meant to be a concave line the curve is so slight in this first part that it appears to be straight. Continue as a concave line and then change to a convex line so that you go through point of Max GZ. After that curve down to go through the Angle of Vanishing Stability.
15. You can now mark and label the “Range of Stability” of the vessel. This is from the Angle of Heel that GZ is initially positive to the Angle of Vanishing Stability. (A vessel at an Angle of Loll will have a smaller Range of Stability than a vessel in stable equilibrium. A vessel in unstable equilibrium will have negative GZ throughout and no Range of Stability.)
16. You can now mark and label the point of Deck Edge Immersion (DEI) also known as the “Point of Contraflexion”. This occurs at the point on the graph
    that the initial concave line turns into a convex line. Often very difficult to see but it is very important.

Question 5

What criteria are based upon IMO SOLAS and MCA Red Ensign Yacht Code with regards to Stability?

Answer 5

For ships stability to be safe, the following must be met:

1. Initial GM Must be no less than 0.15m
2. Max GZ lever no less than 0.20m
3. Max GZ occuring at 30° or more.
4. Area under 30° no less than 0.055 Metre radians
5. Area under 40° no less than 0.09 Metre radians
6. Area under 30° to 40° no less than 0.03 Metre radians
7. Area under the GZ curve should not be less than 0.055 metre-radians up to 30 Degree angle of heel and not less than 0.09 metre-radians up to 40 degree angle of heel.
8. Between 30 and 40 degree angles of heel, the area under the GZ curve should not be less than 0.03 metre-radians.
9. 30 degrees or more the GZ Lever should not be less than 0.20m
10. Max GZ should occur preferably at a 30 degree angle of heel, but no less than 25 degrees
11. Initial GM no less than 0.15m, after correction for FSE.

Question 6

Explain the difference between Dynamic versus Statical Stability!

Answer 6

Static Stability is the measure of the righting arm and the righting moment at any particlar angle of heel.

Dynmaic Stability is the measure of the total work required to incline a vessel from the upright or the work needed to return a heeled vessel to her initial stable position.

Dynamical Stability = Δ x Area under the GZ Curve

Question 7

GZ Curve of Dynamic Stability, comparing high dyanmic and low dynamic.

Answer 7

Question 8

Name another phrase for “Deck Edge Immersion” D.E.I

Answer 8

D.E.I is also known as the “Point of Contraflexion”

Question 9

Compare GZ curves of Stiff, Tender, Standard** and **Loll on a GZ Graph

Answer 9

Question 10

(Change in Freeboard) GZ curve when Freeboard is increased.

Answer 10

A ship with increased Freeboard will have:

• Same initial stability
• Deck Edge Immersion DEI will occur later.
• Greater Max GZ
• Larger Range of Stability
• Point of vanishing Stability occurs later.

Question 11

Change in Beam GZ Curve when Beam is increased.

Answer 11

A ship with increased beam will have:

• Higher intial stability
• Deck Edge immersion will occur earlier than normal.
• Slightly larger range of Stability than normal ship.

Question 12

Formula for under the curve of 30 degrees

Answer 12

Question 13

Explain Downflooding?

How does it happen?

Answer 13

Water getting in from up above from either:

• Spray
• Green water
• Deck edge immersion

This is the Angle of Heel at which the waterline reaches the first opening that cannot be closed weathertight and through which downflooding can occur.

Downflooding cannot be determinded from your GZ Curve.

Question 14

List the REG Yacht Code requirements for Damage Stability.

Answer 14

1. Yacht must remain afloat with any ONe Compartment flooded.
2. Minium Freeboard clearance of 75mm.
3. Equilibrium angle of less than 7° from upright position.
4. Minimum range of stability of 15° either side of the equilibrium angle.