Displacement (or Sectional Area) Sheet (English Units)

Description:This spreadsheet computes hydrostatic volume characteristics relating to station cross sectional areas.  Basically it sums up the area under a sectional area curve to obtain the displaced volume and it takes moments to obtain the longitudinal and vertical centers of buoyancy for an input waterline. 
     If the input waterline is level, the data obtained may be used as an input source for a vessel's "Curves of Form."  Inputs are based on a Lines Drawing with ten stations starting at zero and ending at Station Ten.  This Lines Drawing has customary half stations at each end to compensate for vessel fineness.  The numerical integrations contained in these calculations are based on Simpson's Rules.
     Though optional, this spreadsheet is best utilized in conjunction with a Waterplane Sheet (Product WP-e) and Waterline Input/Output Sheet (Product WL-IO-e).  A further enhancement is dynamically combining this sheet along with a Waterplane Sheet and a Waterline Input/Output Sheet.  The product that combines all these sheets together is called a Waterline Hydrostatics Data Sheet (Product WL-hydro-e).  This later enhanced combination facilitates faster and easier computation for a given waterline.  In the combined case, calculations are more automated, significantly minimizing the data entry input time.

Electronic Document Type:  Microsoft Excel spreadsheet           Cost: $10.00 US funds

Number of Pages: Includes an template (or input) sheet, along with an example sheet, an instructions sheet and a use terms sheet.                   

Inputs:  

• The following dimensional and property input data are required:

  • Clearly document the WL condition being evaluated.  Enter the forward draft (T_FWD), midships draft (T_MID), aft draft (T_AFT) and maximum draft (T).

  • Then enter the station spacing (s). 

  • Enter in half the hull's cross sectional area (SA) for each station.   Note the vessel must be divided into ten stations (this yields eleven cross sectional areas) with a half station at each end (this adds two more cross sectional areas).  This means a total of thirteen input cross sectional areas are required.  Bonjean Curves may be used to quickly determine the cross sectional areas.  They also may be determined by calculation, a CAD program or some other means.

  • For each cross sectional area the vertical distance from the Baseline to the centroid of each cross sectional area is required.  For the template this value is called a vca and thirteen of these values are required.  These values may determined using a Lines Drawing, through a CAD program or through some other acceptable means.

  • For vessel's with overhang; add in the aft overhang volume as well as the longitudinal (from Station 5) and vertical centers (from Baseline) of buoyancy for this volume.  This data is often needed because many vessels that end their LBP (in the Lines Drawing) at the center of the rudder post.  This correction compensates for the volume that is displaced aft of the rudder post, which may be substantial.

  • Finally enter the specific gravity (S) of the water that the vessel is in. If this is in regard to a stability test enter the average specific gravity taken at the time of stability test.

• Optional Input Items:

  • Vessel name, project description, client and calculation date and time.

Outputs:  

• The automatic output generated by this spreadsheet are the displaced volume (V), displaced weight (W), longitudinal center of buoyancy (LCB), and vertical center of buoyancy(VCB).  Note the LCB obtained is the distance from Station 5.

Suggested Reading (see References page for more detail on these items):

• Microsoft Excel user manuals

• Principles of Naval Architecture, Edward V. Lewis, SNAME

• Basic Ship Theory, Rawson & Tupper

• Applied Naval Architecture, Robert B. Zubaly

• Introduction to Naval Architecture, E. C. Tupper

• Introduction to Naval Architecture, Thomas Gillmer and Bruce Johnson

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Minimum System Requirements: Windows 95/98/NT/2000/XP/Vista/Windows7

Sample: A sample document is shown below.