Computing Hydrostatics

We will again be using Rhino 3D to compute many of the necessary hydrostatic variables needed to estimate the drag on the hull. In addition, I've created a spreadsheet to assist in computing several of the coefficients.

Resources

Using Rhino to Compute Hydrostatics

Begin by opening your own design or one of those posted on the 3D Hull Design page. It is easiest to maneuver in the 3D environment if all four views are open. In order to estimate the drag on your design, several parameters must be defined. Many of these terms are explained in the terminology section below

Dimension:
Before dimensioning, orient the canoe such that the forward perpendicular is in line with the z-axis and the canoe is centered about the x-axis. Use the Dimension->horizontal tool in the 'top' window to find the overall length and maximum beam of your design. Use the Osnap option to precisely pick the extreme points. Note: you may need to edit the Dimension->Options to resize the text to a workable size or change the display to to the architectural display (which I recommend to 1/8 or 1/16" accuracy).

Mass Properties:
The x-axis represents the waterline. Guess a reasonable submergence for your design and lower your canoe with respect to the waterline. Use Analyse->Mass Properties->Hydrostatics to compute the displaced volume of water. Continue adjusting the depth of the canoe until you reach a displaced volume that corresponds to your design weight. For a 800lb. load this should be around 12.8cft. Once you have equilibriated the canoe, run the hydrostatic computation again and copy the required information into the Hull Coefficient Calculator spreadsheet.

To determine the maximum immersed section, make sure that the canoe is properly placed with respect to the waterline. Use the Explode command to dis-join the canoe's sections. Copy the maximum section away from the master canoe being carefull to stay on the same y-z plance (maintain the location of the waterline). Draw a line through the section at the level of the waterline and use trim to cut the non-submerged portion of the cross section. Join the line and copied surface and use the surface->patch command to creat a surface on the y-z plane. Finally, use the Analyze->Mass Properties->Area to compute the maximum submerged x-section.

If your canoe was designed without horizontally tilling cross-sections, you'll need to create a surface on the top of the canoe, join all of the sections, draw a surface through the maximum cross section, and use the solid->difference command to create a horizontal cross section of your canoe.

The same procedure can be used to find the submerged transom if necessary.

Terminology

Common Name	Abbreviation	Description
Beam	B, BWL, BOA	The width of the boat. Often refers to the maximum width (BOA) and max width at the waterline (BWL)
Block Coefficient	Cb=V/(LBT)	A coefficient used in computing drag on the hull. Computed by projecting a square surface with dimensions equal to the maximum immersed section along the width of the boat. Equal to the ratio of the actual displaced volume to this projected volume. See Coef Explained 1 (.gif)
Draft	T, H	The maximum distance from the waterline to the bottom (keel) of the boat
Forward Perpendicular	FP	The forward most point on the waterline
Immersed Transom	At	Cross Section of boat at the stern (rear). Usually zero for Canoes
Longitudial Prismatic	Cp=Cb/Cx Cp=V/(LBT*Cx)	Coefficient calculated by projecting the shape of the canoe at the maximum submersed section along the entire length of the canoe. Ratio of actual displacement to projected. Often defined in terms of block coeff and Maximum section coefficient. See Coef Explaied 1 (.gif)
Maximum Section Coefficient	Cx=Ax/(B*T)	Coefficient is ratio of the area at the maximum section versus the plane derived from the maximum beam and draft. See Coef Explaied 2 (.gif)