You are on a supply run to an offshore drilling rig. On board is the cargo listed. What is the height above the main deck of the center of gravity of the cargo?
I. 116 lengths of drill pipe. Each pipe weighs 0.644 long ton. The center of gravity is 1.11 feet above
the main deck.
II. 10 containers 8'L X 4'W X 3'H containing assorted pipe fittings and machine parts. Each container
weighs 1-1/4 long tons, and the center of gravity of each box is 1.35 feet above the main deck.
III. Two 90-fathom lengths of 3-inch diameter wire rope coiled on the main deck. Each foot of wire rope weighs 18.7 pounds. The center of gravity of the coil is 27 inches above the main deck.
IV. 6 pallets of oak planking. Each pallet weighs 2-1/2 long tons with a center of gravity of 2.2 feet
above the main deck.
A. 2.23 feet B. 1.93 feet C. 1.82 feet D. 1.38 feet
I. 116 lengths of drill pipe. Each pipe weighs 0.644 long ton. The center of gravity is 1.11 feet above
the main deck.
II. 10 containers 8'L X 4'W X 3'H containing assorted pipe fittings and machine parts. Each container
weighs 1-1/4 long tons, and the center of gravity of each box is 1.35 feet above the main deck.
III. Two 90-fathom lengths of 3-inch diameter wire rope coiled on the main deck. Each foot of wire rope weighs 18.7 pounds. The center of gravity of the coil is 27 inches above the main deck.
IV. 6 pallets of oak planking. Each pallet weighs 2-1/2 long tons with a center of gravity of 2.2 feet
above the main deck.
A. 2.23 feet B. 1.93 feet C. 1.82 feet D. 1.38 feet
Stability and Trim for the Ship's Officer, 4th Edition, covers this type of question in Chapter 3, "Calculation of the Ship's Vertical Center of Gravity, VCG" on pages 51 to 55, "Using Theory of Moment to Find KG".
ReplyDeleteFirst of all I need to tell you that if you want to look this subject up on the internet it would be better to Google "Weighted Average" instead of "Theory of Moments". "Weighted Average" is the mathematical procedure we are using for this problem. We did a similar one a few months ago as I recall.
To solve this we need to calculate a "Weighted Average" of the cargo on deck.
First we need to identify each weight and its center of gravity above the deck:
I. Pipe - 116 lengths stowed in a block with a given Center of Gravity above the deck of 1.11 feet. Each pipe weighs 0.644 Long Tons (so 116 pipes x 0.664 LT x 2,240 pounds /LT = 167,336.96 pounds
II. Containers - 10 containers x 1.25 LT x 2,240 pounds /LT = 28,000.00 pounds. Each Container has a Center of Gravity of 1.35 feet above the deck.
III. Wire Rope Coiled on Main Deck - 2 x 90 fathoms x 6 feet/fathom x 18.7 pounds/ft = 20,196.0 pounds The Center of Gravity of the Coil is 27 inches or 2.25 ft above the deck.
IV. 6 pallets of oak planking - 6 x 2.5 LT x 2,240 pounds/LT = 33,600 pounds. The Center of Gravity is give as 2.2 feet above the main deck.
Now that we have identified the each groups weights and VCGs (Distance above the main deck) we can do the Weighted Average Calculation.
Solution by Weighted Average Method:
Item Weight x VCG = Vertical Moment
I. 167,336.36 pounds x 1.11 ft = 185,744.03 ft-pounds
II. 28,000.0 pounds x 1.35 ft = 37,800 ft-pounds
III. 20,196.0 pounds x 2.25 ft = 45,441.00 ft-pounds
IV. 30,240.0 pounds x 2.2 ft = 66,528.00 ft-pounds
Total Weight = 249,132.36 pounds
Total Moment = 342,905.02 ft-pounds
VCG of Deck Cargo = Total Moment/Total Weight
= 342,905.02 ft-pounds / 249,132.36 pounds
= 1.376 feet, The best answer is D. 1.38 feet!
Please note: I used pounds and feet because in this problem it was just as easy for me to use these units with my calculator.
One may ask if this question is designed to test your skill of the Weighted Average Method or Units Conversion or your reading skills! This question was easier than the previous similar question posted on Jan. 17, 2018, because the Centers of Gravity of the individual loads were given thus you did not have to use the dimension to determine them.
ANS: DELTA
ReplyDeletemoments / weights
153.08 ft ton / 111.22 ton = 1.376371156
Lots of figuring, I worked the problem in ft. and tons.
This question seemed more about knowing conversions than stability.