“Full and Down” Calculations

“Full and Down” describes the desirable but rare condition in which a vessel has all her cargo space filled and is loaded down to her Plimsoll marks.  Achieving the state of “full and down”  requires some arithmetic.  The old examination bank of questions has three “full and down”Loading to Plimsoll Marks problems, two of which require elementary algebra.  The new examination bank has dropped two of these questions leaving only one relatively simple calculation problem.

Before getting to the questions, we need to define some terms.  “SF” is the stowage factor of a cargo.  It represents the number of cubic feet one (long) ton of a product occupies.  For example, if a cargo has a Stowage Factor of 72, then 2240 pounds (one long ton) of the product will take up 72 cubic feet.  The smaller the Stowage Factor, the denser the cargo.  Feathers have a large stowage factor while lead has a relatively small stowage factor.  A ton of lead occupies much less space than a ton of feathers.

Your vessel has a deadweight capacity of 5000 tons and a cubic capacity of 300,000 cubic feet. You are to load lead, with a stowage factor 18, and cotton, with a stowage factor of 80. If you load "full and down," how much cotton should you load?
A. 1613 tons
B. 2190 tons
C. 2810 tons
D. 3387 tons
Answer: D

Solution:Loading Cargo Hold with Scrap Iron

Maximum Weight: 5000 tons
Available Space: 300,000 cubic feet
Let “x” represent lead
Let “y” represent cotton
x + y = 5000 (tons)
18x + 80y = 300,000 cubic feet
Translate x into y:
x = 5000 – y
Substitute this value of x into second formula:
18 (5000 – y) + 80y = 300000
90000 – 18y + 80y = 300000
90000 + 62y = 300000
62y = 210000
y = 3387 tons of cotton

Your vessel's available bale cubic capacity is 625,000 and her available cargo capacity is 10000 deadweight tons. Disregarding broken stowage, how many tons of pyrite (stowage factor: 13) and how many tons of cork (stowage factor: 150) must be loaded to be "full and down"?
A. 6387 tons pyrite, 3613 tons cork
B. 6721 tons pyrite, 3279 tons cork
C. 7500 tons pyrite, 2500 tons cork
D. 9133 tons pyrite, 867 tons cork
Answer: A

Solution:

Maximum Weight: 10000 tonsPartially-filled container -- cargo damage
Available Space: 625,000 cubic feet
Let “x” represent pyrite
Let “y” represent cork
x + y = 10000 (tons)
13x + 150y = 625,000 cubic feet
Translate x into y:
x = 10000 – y
Substitute this value of x into the second formula:
13 (10000 – y) + 150y = 625000
130000 – 13y + 150y = 625000
130000 + 137y = 625000
137y = 495000
y = 3613 tons of cork
10000 – 3613 = 6387 tons of pyrite

A vessel has a deadweight carrying capacity of 10500 tons. Fuel, water and stores require 1500 tons. The cubic capacity is 600000 cubic feet. Which cargo will put her full and down?
A. Slabs of zinc, SF 7.1
B. Rolls of barbed wire, SF 55.5
C. Barrels of tallow, SF 66.8
D. Bundles of rubber, SF 140.2
Answer: B

Solution:

In order to satisfy both the “full” in terms of capacity and the “down” in terms of weight, we are looking for the cargo that fills the space and meets the weight requirements.  The space available is 500000 cubic feet.  The weight is 9000 tons (10,500 tons less the 1500 tons for fuel, water and stores).

With a stowage factor of 7.1, zinc is too heavy.  500000 cubic feet of zinc weighs 70422 tons, far beyond the allotted 9000 tons.  On the other hand, 500000 cubic feet of barbed wire weighs roughly 9000 tons.  A good fit.

Both tallow (at 7485 tons per 50000 cubic feet) and rubber (3566 tons) fail the “down” requirement.