What is the formula for calculating the angle of loll

what is the formula for calculating the angle of loll

The formula for calculating the angle of loll is tan θ = √2GM/BM, where θ is the angle of loll[1][2]. The formula for calculating GM at the angle of loll is GM = 2(Initial negative GM) x Sec θ[2]. The angle of loll occurs at the inflection point when the GZ or the righting lever becomes zero while transforming from a negative value to a positive value[1]. The other points on the curve where the GZ is zero are when the ship is in a natural upright state that is not disturbed by external forces[1]. The values of GM and BM can be determined by performing a stability analysis of the vessel under given conditions[3]. The formula for calculating GZ is GZ = GM x sin(θ) + 0.5 x BM x tan²(θ) [5]. It is important to note that the value of GM obtained by the above formula will be positive and not negative[6].

Citations:

[1] Angle of Loll calculations - YouTube https://youtube.com/watch?v=3BbL4X-tABs

[2] Angle Of Loll - Knowledge Of Sea https://knowledgeofsea.com/angle-of-loll/

[3] What is Angle Of Loll in Ships? - Marine Insight https://www.marineinsight.com/naval-architecture/angle-of-loll/

[4] Angle of Loll - an overview | ScienceDirect Topics https://www.sciencedirect.com/topics/engineering/angle-of-loll

[5] 2 Plane Area of A Vessel Will Increase in Reality. The Small Angle Formula For GZ Should Only Be Used For Angles of Heel Up To About 5° or 6° | PDF | Classical Mechanics - Scribd https://www.scribd.com/document/458898453/Calculating-Angle-of-Loll

[6] Angle Of Loll- A Thorough Explanation - Sailorinsight https://sailorinsight.com/angle-of-loll-a-thorough-explanation/

By Perplexity at https://www.perplexity.ai/search/eed61dba-1bd7-4fde-80e2-17faed1c33b1?s=m