Your vessel has a displacement of 10,000 tons. It is 350 feet (106.7 m) long and has a beam of 55 feet ( 16.8 m). You have timed it's full rolling period to be 15.0 seconds. What is your vessel's approximate GM?
A. 1.18 feet (0.36 m)
B. 1.83 feet (0.56 m)
C. 2.60 feet (0.79 m)
D. 3.36 feet (1.02 m)
A. 1.18 feet (0.36 m)
B. 1.83 feet (0.56 m)
C. 2.60 feet (0.79 m)
D. 3.36 feet (1.02 m)
C
ReplyDeleteCalculating GM or Metacentric Height -
DeleteThe following formula calculates GM in feet based on the natural roll period of the vessel measured in seconds or T and its beam in feet. A natural roll period is the time between two successive peak roll angles on the same side of a vessel. The most accurate method is to use an average of several roll periods.
GM = (.44 X Beam / T)²
For example, let’s say that a small vessel has a beam of 18 feet and its roll period or “T” is 6 seconds. The calculated metacentric height of this vessel would be:
(.44 X 18 feet / 6 seconds)² = 1.74 feet
With a GM of 1.74 feet, the vessel would be rather tender. With small vessels, the minimum metacentric height should be at least 3 feet and generally over 4 feet is preferred.
Calculating Natural Roll Period Using a Known GM:
We can predict a vessel’s natural roll period or “T” if its GM has been previously determined. Use the following formula:
T = (.44 X Beam) / Square Root of GM
If our vessel’s GM was determined to be 4 feet with a beam of 20 feet then its predicted natural roll period is:
(.44 X 20) / 2 = 4.4 seconds
Longitudinal Stability:
Remember that a vessel has two centers of gravity. We have discussing heeling and listing which involves a vessel’s transverse stability. The other deals with its longitudinal stability which also has a center of gravity (LCG) and a center of buoyancy (LCB). Like transverse stability, we are adding and removing weight in terms of passengers, cargo, fuel, and stores. Instead of dealing with a listing or heeling vessel we are concerned with the trimming the vessel fore and aft. Imagine that a vessel is perfectly balance longitudinally on a point called the Longitudinal Center of Flotation (LCF). When weight is added either forward or after of this point, the vessel either trims down at the bow or at the stern. Usually a vessel sits deeper at the stern (drag) to increase the effectiveness of propulsion. So when a vessel is properly trimmed it preserves its design drag plus ensures that it has proper reserve buoyancy and metacentric height.
I take exception with part of the preceding comment.
ReplyDeleteThe vessel only has one Center of Gravity, G !
A vessel exists in three dimensional space so that one point where all the vessel's weight appears to act is actually located by a Vertical, Longitudinal and Transverse measurements. These are measurements that help locate the individual point known as the Center of Gravity, G.
The Vertical Measurement is the Vertical Center of Gravity which is the distance from the Keel to G, denoted at KG. This is useful concerning problems with Transverse Stability.
The Longitudinal Measurement is the Longitudinal Center of Gravity which can be measured in one of three ways: From the Forward Perpendicular Aft, from the After Perpendicular Forward or about Midships with forward of midships as negative and aft of Midships as positive. You need to consult the Capacity Plan to know for sure. This is useful for problems concerning Trim.
The Transverse Measurement is from the vessels's Centerline measured Port or Starboard. This is useful in doing problems concerning List.
AS far as the best answer I will calculate it metric units:
GM = (0.8Beam/T)squared = (0.8(16.8)/15)^2 = 0.80 so the best answer is C.
Do you agree or Disagree?
What is a Good GM? The best answer in a court of law may be the following:
ReplyDelete"A good GM is the smallest GM consistent with safety."
STABILITY AND TRIM FOR THE SHIP'S OFFICER, 4th Edition,Chapter 5, page 87.
A 80,000 ton Panamax could be considered stiff with a GM of 3 feet or one meter due to the large Righting Moment. On the other hand a Party Fishing Boat of 65 feet may need a GM much larger to create adequate Righting Moment
International Load Line Regulations require a minimum of 6 inches or 0.15 meters of GM.
ReplyDeleteMinimum Required GM on US Flag vessels simply is a test of Wind Heeling on a vessel so that the GM is large enough to Limit the List to no more than 15 degrees or 1/2 the freeboard which ever is less.
Charley. GM = (.44 B/T) squared
ReplyDelete