A bulk freighter 680 ft. in length, 60 ft. beam, with a waterplane coefficient of 0.84, is floating in salt water at a draft of 21'. How many long tons would it take to increase the mean draft by 1"?
A. 64.3 tons B. 69.6 tons C. 81.6 tons D. 116 tons
A. 64.3 tons B. 69.6 tons C. 81.6 tons D. 116 tons
I've had a hard time with these type questions.
ReplyDeleteTPI or "Tons per Inch Immmersion" is the number of long tons (2,240 pounds/LT) that it will take to increase the draft at the LCF one inch.
ReplyDeleteTo solve this question you first need to find the area of the waterplane at the 21 foot draft.
This can be done using the length, beam and the waterplane coefficient given as follows:
AREA of the Waterplane = Length x Beam x Coef of Waterplane = 680 feet x 60 feet x 0.84 = 34,272 Square Feet.
Next you need to find the volume of displacement for the AREA of the Waterplane one inch thick.
To do this we need to convert to cubic feet by multiplying the AREA of the Waterplane by 1/12 of a foot or simply dividing the AREA of the Waterplane in square feet by 12.
Volume of displacement for one inch immersion = (34,272 Square Feet ) / (1/12 foot / inch)
= 2,866 cubic feet / inch immersion
Now to finish the question you also need to know that there are 35 cubic feet of salt water per Long Ton.
(By the way for fresh water, 40 cubic feet per Long Ton is used in similar problems dealing with Fresh Water.)
Now to finish, simply divide the 2,866 cubic feet of additional displacement required by 35 cubic feet / LT.
Ans. (2,866 cu ft) / (35 cu ft / LT) = 81.6 Tons per Inch immersion.
Now for people that sail on vessel using metric units Lets convert it. Keep in mind to find Tonnes/centimeter immersion TPC an inch is 2.54 times larger than a centimeter so the TPC would be about 81.6/2.54 or 32.125 LT/cm to convert this to Metric Tonnes per cm we can do the following
1 Metric ton = 2204.62 pounds and 1 Long Ton = 2,240 pounds, so to convert LT to MT we divide by
(2204.62 pounds/MT) / (2240 pounds /LT) = 0.9842 LT/MT, so
TPC = 32.125 LT/cm / 0.9842 LT/MT = 32.64 MT/cm
C.
ReplyDeleteLxBx (coefficient of W.P.) / 420 (35x12)=420
680x60x(0.84)/420=81.6
Very nicely answered. When a question is Imperial Units any time you see 420 as a constant it the product of multiplying 35 cubic feet per long ton and 12 inches per foot!
DeleteThank you Bill
ReplyDelete