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船舶·稳性
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船舶·稳性
12
engines
船舶浮力与排水量 · Δ = ρ·∇
Ship Displacement & Buoyancy · Δ = ρ·∇
Δ=ρg∇=W · ∇=Cb·LBT=6720m³→6888t · 储备浮力 · 阿基米德
Archimedes' principle: a floating ship's displaced water weighs exactly what the ship weighs
初稳性高 · GM = KB + BM − KG
Metacentric Height · GM = KB + BM − KG
GM=KB+BM−KG · BM=I/∇ · GM>0稳定<0倾覆 · 1.7m@默认
Initial transverse stability: the ship is stable only when the metacentre M sits above G
复原力臂 GZ 与稳性曲线
Righting Arm GZ & the Stability Curve
GZ=GM·sinθ · 复原力矩Δ·GZ · 稳性消失角 · 面积=动稳性
Righting moment = Δ·GZ; for small angles GZ ≈ GM·sinθ, so the initial slope equals GM
船体丰满度系数 · Cb / Cm / Cp / Cw
Hull form coefficients · Cb / Cm / Cp / Cw
Cb=∇/(LBT)=0.66 · Cm/Cp=Cb/Cm/Cw · 瘦快↔肥满
Block, midship, prismatic and waterplane coefficients — how fine or full a hull is
船体傅汝德数 · Fn = v /√(g·L)
Froude number for hulls · Fn = v /√(g·L)
Fn=v/√(gL) · 船体极速Fn≈0.4=1.34√Lwl=24.3kn · 造波峰
The dimensionless speed that governs wave-making and sets the natural hull-speed limit
船舶总阻力分解 · Rt = Rf + Rr
Ship resistance decomposition · Rt = Rf + Rr
Rt=Rf+Rr · Rf随Re/Rr随Fn · Froude比较律 · PE=Rt·v
Froude's method: total = frictional + residuary (wave), with effective power PE
辛普森第一法则求水线面面积
Simpson's First Rule — Waterplane Area
面积=(h/3)(y0+4y1+2y2+…+yn) · 乘子1,4,2,4…1 · 水线面积/∇
Equally-spaced half-breadths → Area = (h/3)·Σ(SM·y), multipliers 1,4,2,4,…,4,1
船舶静水力曲线
Ship Hydrostatic Curves
随吃水T:Δ/TPC=ρAw/100=16.6/KB/BM=I/∇ · 静水力
Displacement Δ, TPC, KB and BM as functions of draft T
纵倾与每厘米纵倾力矩 MCT1cm
Trim & the Moment to Change Trim (MCT1cm)
纵倾=艉−艏 · MCT=Δ·GML/(100L)=108.1 · Δtrim=矩/MCT=18.5cm
Trim = draft aft − draft fwd; a trimming moment changes the trim
船舶自由横摇周期
Ship Natural Rolling Period
T=2π·k/√(gGM)≈0.8B/√GM=10.5s · 刚性短/柔性长
T = 2π·k / √(g·GM) — a larger GM makes a stiffer, faster roll
倾斜试验 · 求船舶重心高度 KG
Inclining Experiment · finding KG
GM=w·d/(Δ·tanθ) · KG=KM−GM=6.90m · 摆锤挠度测θ
A moved weight w·d lists the ship; the plumb reading gives GM, then KG = KM − GM
自由液面效应 · 有效稳性高度的削减
Free Surface Effect · loss of effective GM
FSC=i·ρl/Δ=0.167m · i=lb³/12 · GMeff=GM−FSC · 分舱按n²降
Liquid in a slack tank shifts with heel, raising G by FSC = i·ρ/Δ, so GMeff = GM − FSC