Boat hulls with smoothly curve stems - how to model

I model the surfaces using the Method C above. The untrimmed surface is designed so that it goes through the target stem shape while also considering overall hull shape and fairness. The goal is to achieve the general target shape, not to be obsessive about exactly matching it. After I am satisfied with the hull shape the surface is trimmed. I work in Rhino and the process is efficient. (For the examples above the hull shape was initially created using this method. Then the other versions of how to model the surfaces were created based on that shape.)

 

It's been a long time! I cover many of the details here. I start with the cross sectional area distribution that I want, and the form of the cross sections. The parameters describing the cross sections are varied between the forward and aft perpendiculars using low order polynomials so as to create a faired shape. I calculate the hydrostatics based on a trial value for the parameters and compare that cross sectional area distribution with the desired distribution. Then I scale each section to match the desired area and regenerate the shape. The first image shows a typical area distribution.

To create the stem, I take points from the first four sections and pass a cubic curve through them. Then I extrapolate the cubic curves forward past the centerplane. The intersection of the curves with the centerplane gives me points on the stem. Then I generate a new hull surface that includes those points as well as the ones from the other sections.

The second figure shows the lines of a trimaran hull that was created this way. The stem was tricky because of the curvature of the deck going into the gunwale. The stem actually has to curve back to the deck in order for things to look right. I didn't realize that at first, and my initial attempts at defining a stem always resulted in weird distortions of the hull at the top. It wasn't until I extrapolated the topsides to create the stem that was natural for the topsides shape that I realized what I'd been doing wrong.

The entire process was implemented by linking Excel to Multisurf. The cross sectional area distribution was generated from a formula in Excel. The initial control points at each section were also calculated in Excel. Excel then repeatedly called Multisurf to generate the control points in the CAD model, and to create the hull surface. Excel also called Multisurf's hydrostatics function and Multisurf returned the hydrostatic data to Excel. The control points were adjusted in Excel, and Excel called Multisurf again to generate the points and surfaces. It was really cool watching the CAD screen as all this was going on, seeing the points appear like magic and a fair hull be generated - untouched by human hands.