An Excel© spreadsheet lines development program has been written for a home computer and is available to conference attendees. The program utilizes B-Spline parametric formulations for planar curve definition of the traditional hull lines: body, waterlines and buttocks. The user establishes the basic hull outline, in BSpline curves, by inputting bow and stern overhangs, freeboard at selected points, the draft of the canoe body at selected points, the beam on deck at selected points, and the maximum beam at the waterline. By judicious selections the user will see the resulting hull outline in profile and plan views, and can easily adjust these inputs to gain the desired hull outline. The user works with actual points on the hull rather than B-Spline vertices.
The hull lines are then developed by the Excel program which establishes the hull form defined by the above outlines and satisfying inputs of the conventional hull form parameters: Center of Buoyancy, (Lcb) Center of Floatation, (Lcf) Prismatic Coefficient, (Cp), Maximum Section Coefficient, (Cm) and the Water-plane Coefficient, (Cwp). The lines development is accomplished in two steps.
First, the user employs the Excel Solver to establish a waterline, and Sectional Area curve that satisfy the above parameters. The program accomplishes this by varying the draft at stations two and eight, which adjusts the shape of the center-plane curve without changing the draft, Tc. The solver ensures a “fair” waterline by minimizing the “bending” criterion of the waterline: that is, by minimizing the sum of the squares of d2y/du2 and d2x/du2. Here, y and x are defined by B-Spline formulations in the parameter “u”. The vertices of the B-Spline functions are varied by the Excel Solver to find the minimum bending criterion.
Second, with the Section Area and waterline beam established for each station, the program establishes the shape of each station body curve which satisfies the section area, draft, freeboard and beams on deck and waterline. Fairness is again established by minimizing the “bending” criterion.
Since there are no section areas for stations 10 and the transom, a scheme for constructing a transomgeometrically similar to station 9.5 is provided. Station 10 is established by fairing to the transom.
The program can establish a round bottom hull in about a minute and a half after the input parameters are entered. It is essential however that the hull form parameters be selected judiciously. Clearly Lcb and Lcf must be compatible, and the hull outline must be reasonable in order to gain a fair hull. In this regard the user is provided with automatic input of six different hull shapes that provide good starting points for a design effort. Thus, in a matter of minutes the user can examine an alternate hull shape while keeping selected hull form parameters constant.