I think Mr. Rumsfeld would have made a fine weight engineer because, if you think about it, the quote above could just as well be related to weight engineering. We have the same concepts: Known knowns, known unknowns, and unknown unknowns. Let us break it down:

The known knowns are the easier ones. When you model a pipe and you know the material (thus density), thickness, and length, you know the properties that make up its weight. You also know where the pipe will be located on the vessel. So this, and all similar cases, you should be able to handle quite well.

The known unknowns are a bit trickier, but still not too bad, as we know they are there and we have methods to handle them. In an early phase of the design, the modelled pipe as mentioned above may be just that – a model of only the pipe itself. However, you know that attached to the pipe there will be fittings, valves, and other weight items, not currently modelled but definitely something to account for. These are the known unknowns, as we know they will be there, but we don’t know yet exactly how much and where. Many weight engineers label these weights as “allowance” or ” contingency” and add a percentage to the known weight (in this case the pipe itself) based upon experience and model maturity.

The unknown unknowns represent the weight we know will be there, but we don’t really know what it is or where it comes from. It is sometimes described as a result of the development of the project from contract to completion. When you have accounted for the pipe and the known unknowns, your risk analysis or experience is used to transform this weight estimate to a 50/50 weight estimate (equal chance of final result being higher or lower than estimate). It is another form of ” allowance/contingency” and it may be added as a percentage to the base weight in a similar way as the known unknowns.

Beyond the above (un)known (un)knowns variations, we have the discrepancy that appears when you compare your complete and detailed weight report to the result from the displacement and inclining test report. This deviation is the “dark matter” of weight engineering (science tells us that dark matter in the universe constitutes about 84 % of the total mass; hopefully the results are not that bad for your vessel).

How do we handle this? Ahead of the discovery of it, the way to handle it is to add a security margin to your results. But what to do when you know the size of this mass? That depends on the size of the matter (pardon the pun). Do keep in mind that the inaccuracy of a displacement and inclining test is often given to be around 1-1.5%, and if the deviation is in this range, you really don’t need to deal with it at all. If it is larger than this, the first step is to look at the center of gravity of the missing mass. This can, in some cases, give you an indication of what has been left out from your weight report, or at least some area to look into further. But you may find that you can’t do too much about it except add it to your weight report as a remainder mass – and if so, do spread it into the various weight groups – do not add it as one chunk! Finally, add it to your experience as a weight engineer.

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However, if not abused, statistics is a tool related to facts and stating a truth more than a lie. Furthermore, analyzing statistics can help us predict the future or estimate a value. There are many ways this can be done; perhaps the most typical one is to use a trend line graph set up by past data of whatever development you are studying, whether it is population growth or house prices, and use this to extend the line as a prophecy of the future (looking at the temperature drop these last weeks I can predict winter is coming).

To me, an even more fascinating property of statistics is often referred to as “The wisdom of the crowd.” If you are unfamiliar with the term I strongly recommend that you Google it; I promise you will find many interesting articles. “The wisdom of the crowd” principle is used for an incredible range of subjects, from capital management, business decisions, even politics, and – wait for it – it can also be used for weight estimation of a vessel!

The “wisdom of the crowd” can be explained by the following simple example: Put a jar full of jellybeans on a table. Let a random group of people each take a guess on how many beans are in the jar, and note down the answers. If you pick a random guess from one person and compare with the actual number of beans in the jar, chances are you will not be very close. But, here’s the interesting part: Take the average number of all the guesses and you will most likely be astounded at how close this will be to the true answer. Have a couple of thousand people guess and you’ll probably be spot on. The explanation is as simple as that for every one person guessing a number too low, there is a person guessing a number too high, and on average, they cancel each other’s errors. You’re just an internet search away from reading about actual studies and experiments that confirm this description.

So, how does this relate to weight estimation? Well, I’m not suggesting that you should line up thousands of people and have them all guess the weight of your ship (although that would be an interesting experiment), but there is a more practical and even better approach: By dividing your vessel into several weight groups and doing an estimate of each of them, you will in many ways obtain the same effect. Each weight group represents a ” person’s bean guess” and a higher than reality estimate in one weight group is most likely cancelled by a lower than reality estimate in another weight group.

Now you might object to this and say that even if we are talking about several different weight groups, the guess for each weight group is taken by the same person; and this person may very well have a tendency of leaning too low or too high for his guesses. Therefore the errors would be correlated, thus not giving the desired effect and ending up with a bad overall result. This is a valid objection; however, the estimation for each weight group should be derived from historical data – statistical facts – rather than “guesses” and the correlation between errors should be minimized this way.

To conclude: Divide your estimation into several weight groups to create your own “crowd” and use historical data to obtain uncorrelated “guesses” between the weight groups. Harvest the “wisdom” to get an accurate estimation of the weight and CG of your vessel. And ShipWeight is your software tool to get the job done efficiently.

PS: Another statistical method that is related to this is Lichtenberg’s Successive Principle, which I will discuss in a future blogpost.

The post Make Statistics Work for You – Part 1: Wisdom of the Crowd appeared first on ShipWeight.

A more scientific definition of MOI can be put forth as: A measure of an object’s resistance to changes in its rotation rate. It is the rotational analog of mass.

A change in the rotation rate is also a change to the object’s acceleration. And this is where it gets interesting for a vessel as the MOI says something about the resistance to the vessel’s acceleration around its axes, or to put it very plainly: How “stiff” will the vessel act when it rolls, yaws and pitches.

Of course, there are other factors contributing to this “stiffness”, like hull shape, stability, anti-rolling tanks and so on – but the MOI is the object’s ” stiffness”-property as defined by the mass distribution of the object and not affected by the sea or other external forces.

Thus, the MOI of a vessel is core to being able to calculate seakeeping and sea motion for any vessel. But the task is not very straightforward, as an accurate calculation of the MOI is done by integrating the mass over its distribution, a task that even modern CAD tools will struggle with, even if the vessel is completely modelled in CAD at the point where the MOI values are needed (which rarely, if ever, happens).

This is where the parallel axis theorem (also known as Huygens-Steiner theorem) comes to the rescue. This theorem defines the transferred inertia of an object, meaning the inertia around a different (global) axis than the object’s own (local) axis. It is calculated by squaring the distance between the global and local axis and multiplying it with the object’s mass. The trick to calculate MOI for a vessel then becomes to divide it into several objects and summarize the transferred inertia for all objects as an approximation for the total vessel.

The accuracy of this method depends upon how many objects you divide the vessel into and how large these objects are. A further approximation to the accurate answer can be calculated by adding each of the object’s local inertia to the transferred inertia using the known formula for a solid cuboid as an approximation.

Solid cuboid of height h, width w, and depth d, and mass m

Solid cuboid inertia (source: en.wikipedia.org)

ShipWeight uses the parallel axis theorem, optionally combined with a user-input value of the object’s actual MOI or a solid cuboid approximation, to calculate the MOI of a vessel. How this is done can be seen in our tutorial video #8: Basic Additional Features, available on ShipWeight’s YouTube channel and on our website https://shipweight.com/videos

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