PIAS Manual  2021 Program for the Integral Approach of Shipdesign
Hullform transformation
The GUI allows you to make very precise local changes in hull shape, or to design a hull ab initio. However, it may sometimes be easy to deform or rescale an existing shape globally. This is called hull form transformation — or hull form variation — and Fairway offers also functions for that, which are discussed here. Incidentally, the two methods can also be mixed: first a global transformation, then for example a local modification at a chine or a bulb, and finally again a global transformation to bring the block coefficient or the longitudinal center of buoyancy exactly the desired value.

Attention
The hullform transformation is applied on and with the solid that is single selected in menu .

The hullform transformation functionality is, by the way, also available within the GUI, please see Shift Frames (Lackenby) and subsequent paragraphs. After the transformation option has been selected here, from the Fairway main menu, a selection menu appears with only three options:

Hullform transformation

# Transformation parameter menu

This menu contains the following parameters:

• Length between perpendiculars $$(L_{pp})$$, as given in .
• Moulded breadth $$(B_m)$$, ditto.
• Draft $$(T)$$, ditto.
• Block coefficient $$(C_b)$$ ( $$C_b = \Lambda / (L_{pp} \cdot B_m \cdot T)$$).
• Moulded volume $$(\Lambda)$$.
• LCB (% of $$L_{pp}$$ from $$L_{pp}/2$$).
• Midship coefficient $$(C_m)$$ ( $$C_m = \text{Largest ordinate area} / (B_m \cdot T)$$).
• Transformation type, zoals dat besproken wordt in Transformation types and their properties.

Depending on the chosen transformation type all or only some parameters will be included. If for instance the linear scaling transformation type is selected the hull coefficients will not appear, because they are not modifyable with this transformation type. This menu contains two columns. The first column shows the desired transformation parameter values, as entered by the user. The second column contains the actual values from the solid to be transformed — the single selected solid. Furthermore, the following commands are available:

• [Copy], which copies the parameter values of the ‘solid’ to the ‘desired value’ column.
• [Transform], which transforms a global hullform transformation.

# Specify envelop lines midship section

These ‘envelop lines’ represent the hull limits as applied by the ‘inflate/deflate’ transformation method (as discussed in Inflate/deflate frames). For other transformation types these lines do not have to be given. By specifying these lines, the frames are forced to stay within this envelop. A maximum of ten points can be given, so there is ample space to accomodate knuckles, deadrise etc.

# Transformation types and their properties

The following transformation types are supported by Fairway.

## Linear scaling

All transverse, vertical or longitudinal coordinates are multiplied by a factor. The modifyable parameters are $$L_{PP}$$, $$B_m$$ and $$T$$, the coefficients will not change.

This transformation is also available as , which has the advantage of being undoable, and applies to wireframes as well.

## Shift frames (Lackenby)

The principle of this Lackenby transformation type is that the frames are shifted in longitudinal direction while the frame area and frame shape remain unchanged. This is done in such a way that the desired parameters are obtained. In Fairway this principle has been extended with an optional scaling of the frames, by which variations in breadth and draft are also supported. All points on the hull are shifted when using this option, contrary to the method.

This transformation is also available within the GUI, which has the advantage of graphical feedback and the availability of undo/redo, see Shift Frames (Lackenby).

## Inflate/deflate frames

With this transformation type the desired values of the parameters are obtained by ‘inflating and deflating’ the frame shapes. The points of the frames are shifted perpendicular to the frame shape outwards or inwards. Care is taken to preserve the frame shape as much as possible, without exceeding the extreme hull limits (as represented by the lines as defined in Specify envelop lines midship section). With this transformation type it is possible to change all parameters (only this type can also change midship coefficient $$(C_m)$$). With this type of transformation only points on the frames are relocated, all other points in the network, such as points located on waterlines only, remain unchanged.

This transformation is also available within the GUI, which has the advantage of graphical feedback and the availability of undo/redo, see Inflate/Deflate Frames.

By the way, this transformation type is also used in the hullform transformation module which is applicable on non-Fairway hulls in PIAS, Hulltran.

## Increase/decrease parallel midbody

When selecting this type, on the first line the desired new length between perpendiculars should be given. The second row the location of the aft side of the parallel midbody is entered. The additional parallel body (in case of lengthening) starts at this point and has a constant section equal to the section at this point.

This transformation is also available within the GUI, which has the advantage of graphical feedback and the availability of undo/redo, see Increase/Decrease Parallel Section.

## Shift complete vessel

When using this transformation type the ship is shifted as a whole. With this option you can simply shift, for example, the base, aft perpendiculars etc. After selecting this option, three input fields will appear: longitudinal shift, transverse shift and vertical shift.

This transformation is also available as , which has the advantage of being undoable, and applies to wireframes as well.

### Perpendicular to the shell

With this scheme points of the hull are shifted normal to the hull, with a user-specified positive (outwards) or negative (inwards) offset. The normal-direction can only be determined at the intersection point of two lines. This implies that internal points must be absent for this option and they will be removed by the program automatically. Note that the normal-direction is undefined at knuckles; the program will take the average of the normals around the knuckle. It is unavoidable that undulations in the vicinity of knuckles may occur, particularly with negative offsets (inward).

# Hints for and backgrounds of the transformation process

## Which transformation type to apply?

When performing a ‘real’ transformation (so, not something simple as scaling) the question might arise which transformation method to use: ‘inflate/deflate’ or the frame shifting method of Lackenby. The answer is up to the user, however, the following properties can be mentioned for the two methods:

• With ‘inflate/deflate’ frames remain on their original location, while with Lackenby they will be shifted. That is an advantage of ‘inflate/deflate’.
• Lackenby allows in general somewhat larger transformations than ‘inflate/deflate’. If the ship has a parallel midbody then Lackenby will expand or shrink it as needed. If a ship has no parallel midbody, and it should be become much fuller, then Lackenby will not insert the parallel body. In that particular case it is advised to add a parallel body separately, and then to apply the Lackenby transformation.
• With ‘inflate/deflate’ only the frame shape is modified, points not located on a frame (for example only located in a waterline) are not midified. That is a major disadvantage, which can be relieved to some extent by removing all `internal points' (which are points not situated on the intersection with an other curve), see Remove all internal points from all curves.
• With ‘inflate/deflate’ also the midship coefficient can be modified, which is not possible with Lackenby.

Overseeing this list, for significant transformations Lackenby is to be preferred above ‘inflate/deflate’, except in those cases where the midship coefficient is to be modified. Limits for changes in parameter, which still lead to decent hullforms, cannot be given, those depend on the particulars of the hullform. For example, the block coefficient modification limit of a slender ship will be higher than that of a full ship. That is because the slender vessel has more room available in the middle, and particularly in the ends, which facilitates an even transformation. While with the full vessel there is only limited space to expand the hull form. For this reason no crisp transformation limits can be given, although in practice the following guidelines have emerged:

• maximum change of block coefficient ±0.05,
• maximum change of LCB from $$L_{pp}$$/2: ±4% of $$L_{pp}$$,
• maximum change of $$C_m$$: ±0.02.

It is useless to try to circumvent these limits by re-applying a transformation. For example, two transformations with a block coefficient increase of 0.05 yields the same as a single transformation with a 0.10 increase. These limits are, by the way, not a computer program limitation as such, instead they arise from the combination of hull form particulars and transformation method.

## Parent hulls

Given a collection of parent forms, with the hullform transformation method a hull shape for a new design can be obtained within a couple of minutes. In order to stimulate this design method a library of about twenty parent hulls is available at SARC for general use. These hullforms, from which the majority was created at Delft University of Technology, can be obtained at http://www.sarc.nl/fairway/parenthulls.

# General rotation and scaling

The hullform transformation methods of options have arisen in the naval architectural tradition, and have a specific ship design background. Under the current option the general object transformation methods are collected. This option here are rather rudimentary, and entirely alphanumerical. Currently, work is ongoing on similar functionality in the GUI. For the transformations here apply:

• With function [Transform] the transformation will be executed.
• The transformation is performed on all selected solids (contrary to the conventional transformation as discussed earlier, which is only applied on the single selected solid).

This method is rather simple; for each of the three directions longitudinal, transverse and vertical a factor is given with which all coordinates will be multiplied. There is no fundamental difference between this option and the earlier , albeit the latter is more naval architecturally oriented, because there target values for length between perpendiculars, moulded breadth and draft are applied, while the current option works with multiplication factors (which are applied at each transformation).

This transformation is also available as , which has the advantage of being undoable, and applies to wireframes as well.

Here, must be given:

• An axis around which the object is rotated, which can be specified in two ways; either by specifying two points of the axis, or by the combination of one point and a direction.
• The rotation angle, clockwise (seen from the first point in the direction of the second, respectively in the direction of the axis) is positive.

This transformation is also available as , which has the advantage of being undoable, and applies to wireframes as well.