Ship Form

1. Ship Form Nomenclature & Principal Views Lines & Offsets Coefficients of Form

2. Length Overall (LOA) Length Between Perpendiculars (LBP) Ship Dimensions Forward Perpendicular After Perpendicular Designed Waterline Length (DWL) Beam Designed Waterline Plane Parallel Midbody Afterbody (STERN) Forebody (BOW) Depth Midship Section

3. Length Between Perpendiculars (LBP) Half-Breadth Plan Lines Drawings: waterlines DWL WL2 WL1 Baseline

4. Lines Drawings: sections AP FP Sta 10 9 8 7 6 4 3 2 1 0 After Sections Forward Sections Sta 0 (FP) Sta 10 (AP) MIDSHIP SECTION Sta 2 Sta 8 Sta 6 Sta 4 Body Plan

5. Tumblehome Flair Section Nomenclature Camber Freeboard Depth DWL Beam Half-breadth Draft Deadrise Baseline

6. DWL Sheer Plan Lines Drawings: buttocks DWL PLANE Centerline Plane BP1 BP2 BP3 Butt 1 Butt 3 BP1 Butt 2

7. DWL Sheer Plan Sheer & Camber Sheer DWL PLANE Centerline Plane Camber BP1

8. Lines Drawings • Three sets of drawings define the hull shape Half-Breadth Plan Body Plan Sheer Plan BP1

9. Offsets • Ships lines may be represented numerically in a table • For example

10. Offsets • Half-breadths for different WL’s at a given station may be used to determine the AF of that station (DWL)30’ 25’ 20’ 15’ 10’ 5’ (BL) 0’ B1 = 35 h= 5 A1= ½ (35+33) x 5 = 170 B2 = 33 A2 A3 A4 A5 A6

11. Hull Volume • Section Areas define hull shape • Volumes between sections summed to determine displacement volume,  Midship Section (Station 5) Area below DWL Section Volume V5 = ½ (A5+A4) x d

12. Sta. 10 9 8 7 6 5 4 3 2 1 0 Offsets • Likewise, waterplane areas may be calculated from Offset tables NOTE: The above is distorted because the frame spacing (probably 60’ is not at the same scale as the half-breadths. (Plot to scale below.)

13. Other Hull Form Dimensions • Besides areas & volumes, hull form determines the location of other critical dimensions. • The centroid (geometric center) of the underwater portion of the hull is the Center of Buoyancy B LCB KB • The vertical location of B is measured from the keel (KB). • The LongitudinalCenter of Buoyancy (LCB) is measured from the Forward Perpendicular • The location of B changes with draft (displacement).

14. Other Hull Form Dimensions • Besides areas & volumes, hull form determines the location of other critical dimensions. • The centroid of the waterplane area is the Center of Floatation (F) • Its location (distance from the fwd perpendicular – LCF) is also a function of displacement LCF F

15. Other Hull Form Dimensions • Besides areas & volumes, hull form determines the location of other critical dimensions. • The distribution of waterplane area determines the Metacentric Radius (BM) • The Center of Buoyancy moves along this arc as the ship rolls • With KB known, the Metacentric Height (KM) becomes an important parameter in stability calculations. Waterplane Area M B K

16. MEAN DRAFT (FT). KM (FT) LCF (AFT FP) (FT) LCB (AFT FP) (FT) MT1 (FT-TON) TPI DISPL in S.W. (L.TONS) MEAN DRAFT (FT) 279 1800 268 19000 68 31.1 27 27 278 18000 26 26 67 277 31.05 1700 267 25 25 17000 276 66 31.1 24 24 275 16000 65 1600 31.2 23 23 274 266 15000 Hydrostatic Curves

17. Coefficients of Form • Block Coefficient: CB =  / (L x B x T) AP Beam, B L (along DWL} FP Hull Volume,  (under DWL) Block Volume, L x B x T Draft, T

18. Coefficients of Form • Prismatic Coefficient: CP =  / (AF x L) Hull Volume,  (under DWL) Prism Volume, (AF x L) Midship Section Area, AF

19. Same B & T smaller CM Coefficients of Form • Midship Section Coefficient: CM = AF / (B x T) Beam, B • Note that CM = CB / CP • COF’s are used in the early stages of design to compare characteristics of new design with existing types for estimating performance AF DraftT Rectangle, B x T