Ship Hull Opti­miza­tion: Gen­er­al­ized Lackenby

Most of our maritime CAESES® users probably know about this shift trans­for­ma­tion for opti­miza­tion of ship hulls: the Gen­er­al­ized Lackenby. It has been part of CAESES® for many years now, and it helps naval archi­tects to modify an existing (e.g. imported) hull with just a few clicks. Ok, changing a ship hull is not such a big deal, actually you can do this with any CAD system. The inter­est­ing part of this Lackenby trans­for­ma­tion is that you can shift volume of the hull forwards or back­wards (i.e. in lon­gi­tu­di­nal direc­tion) while auto­mat­i­cally ful­fill­ing user-defined con­straints. Typical con­straints are the lon­gi­tu­di­nal position of the center of buoyancy as well as the change of the dis­place­ment. And, the shift is very smooth! 

As a result, you can quickly optimize a hull shape and maintain the most impor­tant char­ac­ter­is­tics and quan­ti­ties, e.g. to ensure sta­bil­ity criteria and dis­place­ment matters in the next design stage. Check out this opti­miza­tion project of a mega boxer, where the Gen­er­al­ized Lackenby was used for a sys­tem­atic study and a formal shape optimization.

So how does it actually work? 

Initial Hull

For an imported hull geometry, you can directly cal­cu­late the relevant hydro­sta­tic values in CAESES®, in par­tic­u­lar, the sec­tional area curve. This curve is the main input for the Gen­er­al­ized Lackenby. It provides infor­ma­tion about the center of buoyancy and the displacement.

Lackenby Shift

The shift trans­for­ma­tion simply takes this initial sec­tional area curve, plus inputs for the change of dis­place­ment and the center of buoyancy. The volume shift is then con­ducted by applying a smooth shift function in a specific range. In addition, you can option­ally control the start and end tangent of this function. These inputs can be set sep­a­rately for the forebody and the aftbody, respec­tively. The function curve gets cal­cu­lated by the Lackenby itself. As a user, you don’t have to care about this detail — this cal­cu­la­tion is done internally.

The shift function provides the delta value at a specific x‑position, i.e. y(x) = dx(x). This means, at a specific x‑position of the hull, there is a shift of the geometry in x‑direction by using the cor­re­spond­ing y‑value. A positive y‑value means forward shift, and a negative value a backward shift. The zero-ordinate is defined by the hull’s symmetry plane. When you look from the top, you can see the cal­cu­lated shift func­tions — note that they are scaled up by a factor (attribute ​“Delta Curve Factor” in the screen­shot above) for better visu­al­iza­tion, the real values are much smaller:

The Modified Hull

In order to apply the shift trans­for­ma­tion to the existing geometry, you have to create an image of the hull and set the Gen­er­al­ized Lackenby as trans­for­ma­tion. An example is shown below. The x‑sections can be visu­al­ized in the display options of a surface, and the color can be set indi­vid­u­ally in order to have a quick comparison.

More Infor­ma­tion

There is a more recent post about a bulker carrier opti­miza­tion and another about reducing CO2 emis­sions through the usage of CAESES. Inter­est­ing numbers — check them out! 

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