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Stability of Ships 1.4 1.2 b0.6D 0.81.0 StableRectangle 0.20.4 Stability and Othe00.0.0r BodGrapih es 0.1 Un St 0.20.30.4 stable able ρ‘ρs0.50.6 0.7 0.8 0.9 1.0 Vasa on August 10, 1628 by Genick Bar–Meir Stability of Ships and Other Bodies Genick Bar–Meir, Ph. D. 8118 Kolmar Ave Skokie, IL 60076 email:genick at potto.org Copyright c 2021 by Genick Bar-Meir (cid:13) See the file copying.fdl or copyright.tex for copying conditions. Version (0.8.2 September 13, 2022) doi: 10.5281/zenodo.5826326 How to cite this book: Bar-Meir, Genick, “Stability of Ships and Other Bodies”, last modified or Accessed : { } insert the date and version you are using, www.potto.org/downloads.php doi:10.5281/zenodo.5826326 Example: If you are using the latest version Bar-Meir, Genick, “Stability of Ships and Other Bodies”, Last modified: Version 0.8.2 April 13, 2022, www.potto.org/downloads.php doi:10.5281/zenodo.6461784 Alternately use the doi system and ref system of your choice. If you are using older version Bar-Meir, Genick, “Stability ofShips andOtherBodies”, Accessed: Version0.5May4, 2021, www.potto.org/downloads.php, ver 0.5.5 doi:10.5281/zenodo.5523621 ver 0.7 doi:10.5281/zenodo.5523621 ver 0.7.5 doi: 10.5281/zenodo.5826326 ver 0.8.2 current doi: 10.5281/zenodo.6461784 “We are like dwarfs sitting on the shoulders of giants” from The Metalogicon by John in 1159 Please Update Thisbookbecamevictimofitsownsuccesses. Morethan60%ofdownloadsofthisbook are for the old versions because the search engines keep track the previous downloads. Thatis,whentheoldversionwith10,000downloadsfromonewebsiteforexample,like researchgate.net, the new version cannot surface up. The book is released on a rolling fashion. It mean that it released several times during the year. In other words, if you have a copy of the book and it is older than a month, the chances are that you have an old version. Please do yourself a favor and download a new version. You can get the last version from zenodo https://zenodo.org/record/5784893#.Yd1uuYpME-0. While you are there you can download several items: “Basics of Fluid Mechanics”, • “Fundamentals of Compressible Flow”, • “Basics of Die Casting Design”, and • othermateriallike“15YearsExperienceCreatingOpenContentEngineeringMa- • terial” describing the depth of the great depth analytically. likethelargestgastableinworldpublishedbyPottoProjectNFP.Allthesematerialsare authored by the undersigned. If you would like to learn more about this author you can grab the article “15 Years Experience Creating Open Content Engineering Material.” https://zenodo.org/record/5791182#.Yd1v3YpME-0 In the near future the article “20 years of producing open content engineering.” Thank you for using this book. Genick v vi PLEASE UPDATE Abstract Why Abstract Thedoiregistrationofthebookforcedtheexaminationofwhatiswritteninthisbook. This abstract is the result of this examination. Short Abstract This book contains innovative ideas. In fact, the book creates a revolution in the understanding of ship stability. One of the chief problems in ship stability is the rolling (ship rotation) which was treated in the past as a simple pendulum with damping (or without) under external forces (or without such as waves, wind etc). This common mistake in this approach is rooted in the assumption that the location of the rotating point. Mistakenly, it was assumed that the rotation point is at the metacenter, an imaginary point which measures the ship’s stability. In fact, all the books on stability, that were examined, believe in this mistake. This assumption is wrong! Even for stationary conditions! Furthermore, the rotation point (line) is moving absolutely and relativelytothebody(evenforquasi–staticstability). Inotherwords,therotationpoint is floating, depending on the geometry, a fact which was discovered by Bar-Meir. Even with all other mistakes infecting the ship stability, this error can reach to 400% (would youwouldliketobeinshipbuildwithdesignoferrorof400%?). Foranypendulum,the rotation point move relatively to the body, creates two effects: the moment of inertia changesandthependulumbecomesadoublependulum. Thedoublependulumhastwo rotating arms attached to each other. The double pendulum has no regular period and exhibits chaotic behavior. Large sums of money were spent on the finding the natural frequency something that does not exist consequence of erroneous belief. This book is the only book (currently) describing these phenomena. This book also describes the physical transfer mechanism from one rotation mode (like roll) to another (like pitch). The book also describes the transfer mechanism from a linear motion to a rotational motion and the reverse. To appreciate these points consider the status of knowledge of ship stability before this book. There was no physical transfer mechanism and it was supposed to be magic that results from wrong governing equations. This seminal work for the first time answer questions like how the energy and momentum are transferred from one mode to another and why (example roll to pitch or heave to roll). When you know why it something happened you more likely be able calculate it. The reason that these developments, first depicted in this book, is because of vii viii ABSTRACT the new direct examination method. This innovative method also has a byproduct that showsawaytocalculatethecircularsegmentcentroid. Nevertheless,thenewtechnique tocalculatethecentroidisextremelyfarfrombeingthemainandonlyadvantage. This technique examines the ship stability from a physical point of view which is the core usefulnessofthetechnique. Anexampleoftheusefulnessofthismethodisthestability dome. The metacenter technique (the old technique) was centered around the com- mittee(IMO)withoutrealunderstandingofthephysicsofstability. Inotherwords, the metacenter technique is only the beginning (realizing the movement of buoyancy cen- troidwhichwasdiscoveredbytheFrenchengineerPierreBouguer). Theimprovements to the metacenter technique which were added in this book like dimensional analysis are not sufficient enough to improve the metacenter technique to the point where it shows the physics clearly. These statements might look brazen yet, this undersigned belief, they are not enough to show the advances made in this book. Long Abstract Thisbookdealswithstabilityoffloatingbodies. Theapproachtakeninthisbookisthat oflookingatthephysicalpointofviewonthestability. Thismeansthatinsteadlooking atregulations,thebookexamineswhythethingsbehaveinacertainway. Forexample, the book does not start with theGGGMMM (metacenter approach) but deals with the direct approach (today standard approach angle in angle out). While this difference looks symbolic at first, the results are profoundly different. For example, in the common approach it was assumed (actually it is deeply entrenched belief “relic of the past”) that a change in the cross section liquid line is irrelevant. As results, an upside triangle and downside triangle have the same stability. Or even more egregious is the fact, the believe in the metacenter approach which yield the “fact” that the moment of inertia of ship is fixed which could be 400% error. You do not want to be under or over bridge with this kind of error. Here in this book, it was found that during the floating body tilting, the rotation point changes according to the tilting angle. The rotation location isindirectlybelievedtobeinthemetacenterapproachinMMMandMMMisassumedtobeat a fixed point for small angles. These two assumptions are wrong, the rotation point is notaroundmetacenterandtherotationisnotfixed(onlyundercertaincircumstances). Even in the special cases where the rotation point is fixed, moment of inertia is not around the gravity centroid or metacenter but at point AAA. The discovery, that the rotation point (location and movement), provides the ability to describe and articulate how energy is transferred from one mode to another. For example, when floating body undergoesheaveitchangesthemomentofinertiahencechangetherequiredcalculation for roll mode. Thismethod,usedinthisbook,demonstratesthattheturningpointofthefloating body is at point AAA on the liquid line which can move around. Are these discoveries important? The answer is yes for most important aspects. Both methods yield the same results for the prediction of the floating bodies stability, Yet, the weakness of the metacenter method, is that even with the dimensional analysis improvement it miss major effects. For example, is a ship with 1[m] GGGMMM and a small boat same GGGMMM are