Prismatic coefficient study
by Joseph Oster
It's interesting to note that the Cp (prismatic coefficient) of a sphere is 0.52, either fully or only half submerged! Clearly prismatic coefficient without LB (Length/Beam ratio) and other factors, doesn't adequately describe a hull's shape.

Leaving the length, beam and draft (middle cross section) the same while allowing displacement to go up with prismatic coefficient (Cp); in this case, going from Cp=.62 to Cp=.70 gains 61 lbs. displacement (12.5%) at the waterline shown.
compare - bow on
PPI (lbs./inch immersion) goes from 71 to 78.

compare - topsides


Based on this earlier sketch of a beach proa hull, August, 1999. The sides of this hull are flat panels, the bottom a "surface of revolution".
The entire hull shape, including keel rocker is determined by the single curve from midsection to bow, as seen from above.


MultiSurf Hydrostatics   Model file: prismatic_60  15-Jan-2002  16:51:39
W.L. Length     19.00 ft            W.L. Beam          1.00 ft      
W.L. Fwd. X     -9.50 ft            Draft              0.75 ft      
W.L. Aft  X      9.50 ft      
      Displacement
Volume          7.608 ft^3          Ctr.Buoy. X        0.00 ft      
Displ't.        487.1 lb            Ctr.Buoy. Y        0.00 ft      
LCB (% w.l.)     50.0               Ctr.Buoy. Z       -0.30 ft      
      Waterplane
W.P. Area       13.36 ft^2          Ctr.Flotn. X       0.00 ft      
LCF (% w.l.)     50.0
      Wetted Surface
Wetd.Area       30.48 ft^2          Ctr. W.S. X       -0.00 ft      
Ctr. W.S. Z     -0.39 ft      
      Initial Stability
Trans. GM       -0.19 ft            Trans.RMPD        -1.66 ft-lb   
Longl. GM       33.97 ft            Longl.RMPD       288.78 ft-lb   
      Coefficients
Waterplane      0.704
Prismatic       0.626
Block           0.536
Midsection      0.856
Disp/length      31.7

MultiSurf Hydrostatics   Model file: prismatic_70  15-Jan-2002  16:43:34
W.L. Length     19.00 ft            W.L. Beam          1.00 ft      
W.L. Fwd. X     -9.50 ft            Draft              0.75 ft      
W.L. Aft  X      9.50 ft      
      Displacement
Volume          8.555 ft^3          Ctr.Buoy. X        0.00 ft      
Displ't.        547.7 lb            Ctr.Buoy. Y        0.00 ft      
LCB (% w.l.)     50.0               Ctr.Buoy. Z       -0.30 ft      
      Waterplane
W.P. Area       14.65 ft^2          Ctr.Flotn. X       0.00 ft      
LCF (% w.l.)     50.0
      Wetted Surface
Wetd.Area       32.52 ft^2          Ctr. W.S. X       -0.00 ft      
Ctr. W.S. Z     -0.41 ft      
      Initial Stability
Trans. GM       -0.20 ft            Trans.RMPD         -1.9 ft-lb   
Longl. GM       36.94 ft            Longl.RMPD        353.1 ft-lb   
      Coefficients
Waterplane      0.773
Prismatic       0.703
Block           0.602
Midsection      0.857
Disp/length      35.6

NOTE: For a definition of these terms, see: Ted Brewer Presents A Primer on Yacht Design

Also:
  • Ideal Boat Hull Calculator

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