Final Exam Formulas - Naval Architecture | AOE 3204, Study notes of Aerospace Engineering

Download Final Exam Formulas - Naval Architecture | AOE 3204 and more Study notes Aerospace Engineering in PDF only on Docsity! Formula Sheet AOE 3204, Naval Architecture CB = ∇ LBT CM = AM BT CP = ∇ AxL CW = AW LB CX = Ax BT AW = 2 ∫ L/2 −L/2 ydx LCF = MmidAW Mmid = 2 ∫ L/2 −L/2 xydx IL = Imid −AWLCF 2 Imid = 2 ∫ L/2 −L/2 x 2ydx IT = 2 3 ∫ L/2 −L/2 y 3dx; For a box barge: IT = 1 12LB 3 As = 2 ∫ T 0 ydz ∇ = ∫ L/2 −L/2Asdx = ∫ T 0 AW dz M∇mid = ∫ L/2 −L/2 xAsdx LCB = M∇mid ∇ M∇K = ∫ T 0 zAW dz ∆ = ρg∇ or ∆m = ρ∇m KB = M∇K ∇ BM = IT∇ TPI = AW420 (US units) TPC = AW97.56 (SI units) GZ = GM sinφ, for small angles tanφ = GG ′ GM = wd ∆GM , for small angles Free surface correction: GGv = w.ggv ∆ ; ggv = it v ; so, GGv = it ∇ ρt ρs Vertical correction due to CG at different height than pole height: GZ = GcZc ±GGc sinφ Transverse shift in G: G′Z ′ = GZ −GG′ cosφ BML = IL ∇ tan θ(in terms of drafts) = tL = f F = a A = m LCF = x X t = TA − TF tan θ(in terms of shifted weight) = GG ‘ GML = wd∆GML KML = KB +BML = KG+GML MT1 = ∆GMLL(in inches) GML ≈ BML t = wdMT1 Small weights method for trim: dtx = s+ x = w TPI + X L t = w TPI + X L wd MT1 Note: mid is used for midship. 1