Understanding Ship Trim and Draft Changes
Explore the dynamics of ship trim and draft changes, from the effects of weight distribution to the shift in center of buoyancy. Learn about the practical implications and key equations governing these principles in naval architecture.
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Presentation Transcript
Trim Problem Section 3.6
Focus X-axis Change in LCG Trim Problem
Big Picture Consider a ship floating on an even keel, that is, no list or trim _. When a weight, w, is added, it causes a change draft _. Equation Sheet, Ch. 3
Big Picture The ship will pivot about the center of floatation (F) The change in draft will be evident in a change of draft both forward and aft Deeper more draft (+) Shallower less draft / more out of water ( Shallower less draft / more out of water (- -) ) Deeper more draft (+) Taft _. F Tfwd The difference of the change of the aft draft and the change of the forward draft is the change in trim: Trim = Taft - Tfwd
Change in Trim Graphically, it looks like this. First, the ship is represented with a line representing its initial state: FP AP O )( _. F As weight is added, the the ship rotates about F: O )( FP _. AP F
Ship Trim Definitions If ship is trimmed by the stern Bow is up Taft > Tfwd Trim is (+) If ship is trimmed by the bow Bow is down Taft < Tfwd Trim is (-) Equation Sheet, Ch. 3
Key Equations There are two aspects to consider when finding the change in draft: 1. Change in draft due to the parallel sinkage (PS) of the vessel due to the added weight, w : Equation Sheet, Ch. 3 TPI, Tons Per Inch Immersion is a geometric function of the vessel at a given draft and is taken from the Curves of Form The added weight, w, will cause the vessel to sink a small distance for the length of the entire vessel We assume that the weight is applied at F! This assures that the sinkage is uniform over the length of the ship
Key Equations 2. Change in trim due to the moment created by the added weight at a distance from F, or w*l : Equation Sheet, Ch. 3 MT1 , or the Moment to Trim 1 , is also from the Curves of Form The weight, w, at a distance, l, from the center of flotation, F, creates a moment that causes the ship to rotate about F This rotation causes one end to sink and the other end to rise The degree of rise or fall depends on the location of F with regard to the entire length of the ship as given by Lpp We need to find how much of the trim is aft and how much is forward
Key Equations The calculation for change in trim can then be used to calculate a change in draft both forward and aft: ????? ???? ??? ????? ???? ??? ?????= ?????= Equation Sheet, Ch. 3, combined into 1 equation with these 2 applications
Key Equations So we know ????? and Lpp, but what is ???? and ???? ? ????? ???? ??? ????? ???? ??? ?????= ?????= ???? - distance from the FP to F ???? - distance from the AP to F This sets up a ratio of similar triangles to solve for ????? and ????? The value for ???? and ???? will be found while drawing a Trim Diagram
Key Equations Putting it all together ????? ???? ??? ????? ???? ??? ?????= ?????= ??,???= ?0,??? ???? ????? ??,???= ?0,??? ???? ?????
Trim Problem Goal is to determine new drafts (T) both forward and aft Procedure: 1. Calculate impact of weight addition/removal to mean draft using TPI. 2. Calculate impact of weight addition/removal to trim at given distance from center of floatation 3. Calculate trim effect on fwd and aft drafts separately 4. Separately add mean draft impact to trim effects to determine final drafts fwd and aft.
Equation Sheet Familiarity ????? ???? ??? ?????= ??,???= ?0,??? ???? ????? ????? ???? ??? ?????= ??,???= ?0,??? ???? ?????
Trim Diagram Demonstration on the board of properly labeled trim diagram
Example Problem 0. Draw and Label Trim Diagram:
Example Problem 1. Calculate impact of weight addition/removal to mean draft using TPI
Example Problem 2. Calculate impact of weight addition/removal to trim at given distance from center of floatation
Example Problem 3. Calculate trim effect on fwd and aft drafts separately
Example Problem 4. Separately add mean draft impact to trim effects to determine final drafts fwd and aft.
