In the last section we looked at the line drawings. They are useful, but not quite. Let us say I have line drawings on paper (A4), I have to scale it up / convert it to numbers in order to design a boat. Model or scaled up, these line drawings need to be converted to a set of numbers.
These numbers are represented in a table called “Offset Table”. Practically, if you just have the Offset Table, you can start building a hull from scratch. However, for the first model I designed, I didn’t get the offset table. So, here is how I converted the line drawings to an offset table.
I started off with this one — the Sacoleva Griego — a fishing boat. As you can see, it is not a very big one as vessels go (12.6m ~42ft long). I took this from a blog linked to pinterest through random search for “ship line drawings”. It was free. More importantly, it was simple as well. There were six water lines and 10 station lines on this design. Compare this with Hercules we used to demonstrate in the previous article in this series.
When you buy a ship plan, you get these line drawings and something called an offset table. The offset table is the starting point for all ab initio hull design. With free designs like these, you don’t get the offset table. However, it is possible to go from the line diagram to offset table with nothing but a standard ruler. We will see how. Along the way, we will also see what an offset table is and why it is useful.
To understand offset tables, we need to understand offsets. let us start with a simple set up of four curves: two in the XY plane, and two in the XZ plane. (see illustrations below).
X-Y plane view
X-Z Plane View
To understand the grid in 3D, see the perspective view below
Few things to note from the three screenshots above:
- The curves in the same plane family (say, X-Y plane) are offset by a certain distance in the third dimension. This is true of any plane you choose. In other words, every curve lies in its own plane, but the planes for a given set of curves are parallel.
- The curves in orthogonal planes (X-Y and X-Z are orthogonal) intersect. Every curve in the X-Y planes will intersect with every curve in the X-Z planes.
- The points of intersection form a mesh (in the third pic above, you see a box shaped grid. That is a closed polygon. A collection of such polygons finally makes up the hull (in a full line diagram).
- In each curve, every point is offset from the principal axes of the curve by certain values.
Since curves in the orthogonal planes necessarily intersect, every curve will have N intersection points, which correspond to the N curves in the orthogonal plane. And these intersection points (of all curves) mark the surface of the hull.
Let us convert the geometry speak to drawing lines. Every curve in the X-Y plane is a waterline. Every curve in the X-Z plane is a station line. If you take the set of all station lines, they all line in parallel X-Z planes with a Y offset. Similarly, all waterlines lie on parallel X-Y planes with a Z offset. Every waterline necessarily intersects with all station lines that pass through that Z value (more on this later). Every station line necessarily intersects with waterlines that pass through the corresponding Y value.
Imagine a point where a station line and a waterline intersect (circled in the img below:
We can view this point in two ways. When viewed from the X-Z plane, this point is some distance away from the Y axis. When viewed from the X-Y plane, this point is some distance away from the Z-axis. The combination of this information is known as its (the point’s) offset. A collection of such points (intersection between water lines and station lines) is called the offset table.
Going back to the line drawing of Sacoleva Griego:
We are viewing it from the Z axis and the curves you see on the bottom half are the waterlines. The straight vertical (Y-axis) lines you see are the Z axis view of the station lines. We set the X axis to the middle line of the ship running bow to stern, and the origin of the X-Y axis to the front end of the hull. From the origin, we can calculate the “X-offset” by measuring the distance of each vertical line from the origin. This set of X- distances define the X-coordinate for all waterlines. The next is a more tricky (or laborious) part. For each station line (vertical line here), measure the distance from the X axis (middle line) to the point where the vertical (station) line intersects with the waterline (curve). My preference is to do this for a station line across all waterlines, and then move on to the next station line. You can do it on a waterline to waterline basis. Mark down these as Y values corresponding to every X value.
In the end, you should have a table of X-Y coordinates, each corresponding to a point on a hull. More importantly, every row of X-Y coordinates in this table will represent the outline for the hull at a certain Z-value. Funnily enough, when we set the Z-values for these curves, it will automatically solve for the shape of the station line too. For the Z-values, we need to go back to the Station Line view (from above).
This is where everything comes together: you already have part of the offsets for the station lines (the Y offsets you calculated before, now become the X values for the station lines). You also see some horizontal lines. These are the waterlines (the curves you saw above). The heights of the horizontal lines from the base (the dotted horizontal line at the bottom) are the Z coordinates for the water lines. Measure the heights of the horizontal lines and move the curves (above table, each offset row) to the corresponding Z-height. Voila, you have your hull coordinates in 3D. This table, that speficies the offsets of the waterlines and stationlines, is called the offset table. In reality, it looks something like this.
For a visual and interactive understanding of this post — see here. The author of this interactive plot (not me) has done a great job of putting together the elements of the offset table.
An example of a “original” offset table is given below. Note — this is not that of Sacoleva Griego.
Here is a dirty offset table I created for Sacoleva Griego, based on the line drawing I have posted in the blog [it is dirty because it is badly annotated, and near impossible for anyone else to use. On the plus side, it a demo of how quickly one can go from line drawings to usable offset tables].
For a high resolution line drawing, use this link. [disclaimer — I found the high res TIF from a modeling forum; I often lose track of the original site. If you are the site owner / owner of the plan, please leave a note below. I will add the URL here. Thanks.]
Another important (conceptually easy) part: scaling. The measurements you have taken are for a hull that is the size of your printed image. If you want it sized up or down, simply multiply the offsets (x, y and z) by the scaling factor. Note that uniform scaling is essential to keep the shape of the hull intact.
In the next part, we will go from offset tables to design on FreeCAD; and from design to prints. We will also discuss a few design elements I had to improvise / iterate.
Happy offsetting.
