Utilizing Curves of Form in Naval Architecture
Explore the application of Simpson's Rule in solving geometric properties of ships through Curves of Form. Learn about calculating Displacement, LCB, KB, TPI, WPA, LCF, MTI, KML, and KMT using mean draft values. Discover the significance of TPI in inch immersion and parallel sinkage in saltwater. Dive into naval architecture principles and assumptions to enhance your understanding.
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Presentation Transcript
Curves of Form Section 2.10
Curves of Form Remember all those calculations we did using Simpson s Rule? Now that you ve proven you can solve for them, they are available to you via the Curves of Form! Curves of Form A graph which shows all the geometric properties of the ship as a function of ship s mean draft Displacement( ), LCB, KB, TPI, WPA, LCF, MTI, KML and KMT are usually included Values from curves Used in further calculations ** 2 Assumptions ** 1. Ship has zero list and zero trim (upright, even keel) 2. Ship is floating in 59 F salt water
Curves of Form Naval Architecture for a given Draft Hull Shape Value Enter on left (draft), unit value up or down from curve Mean Draft Curve Units Convert units to value with legend Numerical Value Mindset Practice 1 Nickel ___ cents 1 Quarter ______dollars 3 Nickels ___ cents 15 5 0.25
Values from Curves of Form 1. Displacement ( ) aka Weight Assume ship is in the salt water with = 1.99 Unit of displacement : long ton (LT) 1 long ton (LT) =2240 lb ?? ?2 ??4 2. LCB Longitudinal Center of Buoyancy Distance in feet from reference point (FP or Amidships) 3. VCB or KB Vertical Center of Buoyancy Distance in feet from the Keel to Center of Buoyancy (B)
Values from Curves of Form 4. TPI (Tons per Inch Immersion) aka Immersion Long tons required to obtain one inch of parallel sinkage in salt water Parallel sinkage: the ship changes its forward and aft draft by the same amount so that no change in trim occurs Trim : difference between forward and aft draft of ship On Equation Sheet (Ch.3) ?? ??? Unit of TPI : Note: for parallel sinkage to occur, weight must be added at center of floatation (F)
TPI (Tons per Inch Immersion) aka Immersion 1 inch Awp (sq. ft) 1 inch Assume side wall is vertical in one inch TPI varies at the ship s draft because waterplane area changes at the draft
TPI AWP On Equation Sheet (Ch.3) On Equation Sheet (Ch.3)
TPI AWP You will not use this from equation sheet, just a reminder that TPI and AWP are directly related. TPI TPI and AWPare directly related Single Curve on the Curves of Form with different conversion factors 5. AWP (Waterplane Area) Area (in square feet) of the waterplane
TPI in an Equation How could we calculate change in draft due to parallel sinkage? On Equation Sheet (Ch.3) More to come on this in Chapter 3!!
Moments Review What is a moment? A force applied over a distance Moment = Force x Distance (M = F x d) Units: foot pounds or foot - LT Negative
Values from Curves of Form 6. Moment/Trim 1 inch (MT1) Moment to change trim one inch The ship will rotate about the center of floatation (F) when a moment is applied to it The moment can be produced by adding, removing or shifting a weight some distance from F Unit : ?? ?? ??? AP l FP 1 inch F
Moment/Trim 1 inch (MT1) How could we calculate change in trim due to a weight addition/removal/shift? On Equation Sheet (Ch.3) More to come on this in Chapter 3!!
Moment/Trim 1 inch (MT1) When MT1 is due to a weight shift, l is the distance the weight was moved LCF l New waterline Change in Trim due to a Weight Shift More to come on this in Chapter 3!!
Moment/Trim 1 inch (MT1) When MT1 is due to a weight removal or addition, l is the distance from the weight to F FP AP l 1 inch F W Change in Trim due to a Weight Addition/Removal More to come on this in Chapter 3!!
Values from Curves of Form 7. ??? Distance in feet from the keel to the longitudinal metacenter 8. ??? Distance in feet from the keel to the transverse metacenter ???& ???are values On Curves of Form Learn about meaning in Chapter 3! 9. LCF (Longitudinal Center of Floatation) X component of center of floatation (F)
Curves of Form Where to find them on the EN400 Page https://www.usna.edu/NAOE/academics/en400.php At the bottom, in the links to the different ship types! Will need to look up to solve homework problems!
Curves of Form Example Problem A YP has a forward draft of 9.5 ft and an aft draft of 10.5ft. Using the YP Curves of Form, provide the following information: = _____ KMT=____ WPA= _____ LCB=____ LCF= _____ VCB=____ TPI=____ KML=____ MT1 =_________
Curves of Form Example = WPA = LCF = TPI = MT1 = KMT = LCB = VCB = KML = Draft Curve Units Convert Numerical Value Draft Curve Units Convert Numerical Value
Curves of Form Example = 192.5 2 LT = 385 LT = WPA = 235 8.4 ft = 1974 ft WPA = LCF = 56 ft from FP LCF = TPI = 235 .02 LT/in = 4.7 LT/in TPI = MT1 = 250 .141 ft-LT/in = 35.25 ft-LT/in MT1 = KMT = 192.5 .06 ft = 11.55 ft KMT = LCB = 56 ft from FP LCB = VCB = 125 .05 ft = 6.25 ft VCB = KML = 112 1 ft = 112 ft KML = Draft Curve Units Convert Numerical Value Draft Curve Units Convert Numerical Value
