Basiliscus Curve of Sectrional Areas

I have a question for Tom Speer if you still browse this forum. I've been reading your very interesting CSYS paper on the Basiliscus project. How did you derive the equation for the curve of sectional areas? I can't type it here for the benefit of others, as the text editor is too basic, but click here to see it.
I have used the equation as the basis for a parametric hull form generator spreadsheet, adding in a submerged transom area and (if needed) a parallel midbody part. As it was developed for ships rather than yachts, I currently have no capability to set a rocker profile (just a straight rake of keel and cut up at the skeg), but this will be done when I get the chance. I wanted to thank you for your excellent paper and ask you about the background to the equation. Did you develop it or is it published elsewhere? How did you select the form of the equation? Why, for example, 3/8 Cp, not 5/16 or 10/11? It seems to work, but I'm curious and would like to know more before about it.

Does anybody else use a target curve of areas as an input when designing the hull, or is it just an output to check? If you do, what curve shape do you use?

 

I'm interested in seeing a graphical example. Do you have a link?

 

Oops, sorry! Forgot to attach the link.

http://www.basiliscus.com/CSYSpaper.pdf - pages 10 and 11

 

PI
You may have to mail or private message Tom to summon him.

Part of the design spiral and one of the inputs definately, I compare it with a reference set after generating the basic hull, then I change the hull if the curve is not to my liking. I check that the rate of change is ok for the entry and exit and that the max area is aft of midships by the desired amount. I also look at the curve for one or two angles of heel and for some semblance of hull speed smooth water surface. Although when you have done this a few times you can make a pretty good call just from experience.

The curve in itself does not tell you much about how the areas are being developed. For example attempts to reduce resistance in models by fairing the hull to smooth the bumps crated by the keel have generally had negative results. A lot of aircraft theory doesn't work for us because the reynolds numbers are so much higher.

Remember a boat at sea is in a very dynamic open system and I feel that characteristc equations for vessels operating in such a medium are no more than a place to start refining your models from. As the vessel size goes up or on sheltered water, complex models produce much more usable results.

Cheers

 

Sorry for not responding earlier - I just got home from a 35 day trip.

This writeup describes the origin of the cross sectional area. I've seen the same curve, minus the shift in the longitudinal center of buoyancy, used in a paper from Japan on optimal area distributions for ships (I'll see if I can find the precise reference).

More than anything, it is just a geometry that seems to produce decent hull forms with a minimum of input parameters. I can't claim that it has any special hydrodynamic properties.

It was selected using the TLAR principle. (TLAR = "that looks about right")

There are some limiting values for Cp. For this distribution, values of Cp less than pi/7 (0.45) will result in non-physical shapes, with negative areas near the ends. Setting Cp greater than 15pi/64 (0.73) will result in necking in the waist of the hull, forming two bulges instead of a single maximum beam.

For wider hulls than I was using, Larsson & Eliasson ("Principles of Yacht Design") show 0.59 as the optimum Cp for a Froude number of 0.4, and 0.56 as optimum for Fn=0.35.

I went with a higher Cp because as it was a multihull and therefore operating above hull speed much of the time, I definitely wanted a length/beam ratio more than 8:1 and preferably more like 10:1.

 

Many thanks for the reply Tom. It looks like I'll have to read the paper again - this time with my eyes open!