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by J. Vazquez

October 30, 2019

This article is a follow-up to the one in our Summer 2019 newsletter that included a “for fun question” on whether or not the actual vertical position of a weight being lifted by a crane on a floating barge changes the stiffness of the barge.  


I am happy to report that the question drew a decent amount of interest, and I received almost 10 responses.  As I predicted, not all answers were the same, as this topic has always been a source of misunderstanding in our field.


For those of you who don’t remember the question, here it is:


Consider a floating barge with a cargo weight being lifted off the deck using a crane (see sketch below).  Once the cargo weight is lifted off the deck, does the system become more and more tender as the cargo weight moves higher and higher from the deck?  


The correct answer is No, the system does not become any more tender as the lifting cable is reeled in.


Right Photo Source 

From the time I started writing the original article and preparing the question, I wondered how I’d present the answer, so as to eliminate any doubts that I had the correct answer.  


I am lucky that someone else provided a detailed answer that I believe will do the trick.  So, please CLICK HERE to see the answer provided by Roy Cottrell, a good friend, current collaborator/consultant and former co-worker of mine.   Roy is president of Cottrell & Cottrell.  You can find more info about Roy from the C&C website at this location  


Roy - thank you very much for taking the time to prepare this detailed response.


Now, a more interesting question.


Consider an ideal container with the following properties:

  1. Container Shape:  perfect 1m x 1m x 1m cube

  2. Container’s Mass:  20 Kg, with CG located at 0.05m above the bottom (i.e., the bottom flat is much heavier than the walls).

  3. Container’s top is open (so that weights can be added)

  4. Container floats freely on fresh water (with assumed density of 1.000 MT/m^3). 

  5. Container’s wall and bottom thickness is negligibly small (yet stiff enough to maintain its perfectly cubic shape at all times).

  6. Container has internal vertical walls dividing the cube into four equal compartments having prismatic shape (0.5m x 0.5m x 1m).  Therefore, each compartment has a maximum volume capacity of 0.25m^3.  These internal walls are assumed to have negligible thickness and yet stiff enough so as to maintain their shape throughout our experiment.

I offer the below sketch, with prescribed orientation and compartment naming.


Now, the question.  What are the roll and pitch angles of this container when

  1. a single container compartment (say, compartment 1) is filled with 0.125m^3 of fresh water (i.e., half of its maximum capacity)?

  2. three of the 4 container compartments (say, compartments 2, 3 and 4) are filled each with 0.125m^3 of fresh water?

If the calculated angles are larger than physically possible (i.e., they’d cause outside water to start getting into an open compartment), then answer these questions:  


To what percentage of maximum capacity can

  1. a single container compartment (say, compartment 1) be filled before outside water starts coming into the compartment?

  2. three of the 4 container compartments (say compartments 2, 3 and 4) be filled before outside water starts coming into a compartment?  (For this question, assume all 3 compartments have the exact same amount of water).


Let’s aim for accuracy to 2 decimal places in the calculated roll/pitch angles.


I look forward to getting your answers!

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