Hello Gents
Jim Slade had asked me to demonstrate the process of fairing hull stations using diagonal splines. Instead of choking his inbox, I thought maybe I�d post as a tutorial here, in the event that others may be interested in this process as well. The intent of this tutorial is to display how the use of both diagonals and the concept of forshortened views, both techniques used for centuries in hand draughting, can be updated to CAD use to develop fair compound surfaces.
PART 1
For this tutorial, I�ll be starting with these old set of stations for a DLG. These were entered and generated from a table of offsets taken from the loft floor at the shipyard. (for anyone wishing to learn how to enter a table of offsets, let me know. I may consider doing another quick (meaning long winded) demo on how to generate a point cloud from them)
Keep in mind, you can click on the screenshots to see larger versions..
Doing an entire hull with one surface is near impossible with modern hulls, due to the amount of twist, and artificial features such as hollowed runs, skegs and bulbous bows. So, it is best to break the hull into sections. For the first section, I�m choosing to do from Station (Sta) 2 to Station 10 (midships). Note, I�m not starting at the extreme bow or stern itself. The reason being, that it allows me to have a couple of stations past each end, despite not being faired themselves, to help initiate the proper end conditions for the diagonal splines. To achieve this I have included Sta � to Sta12.
This shows a view of my Stations from below the bow. While my screenshots don�t show color very well, the ends of the surface I intend to generate are bordered by the yellow stations. As I continue, I�ll be using the �cubic spline� functions to generate my splines. The issue with cubic splines, is that unless you have a way to define the end conditions, such as using a tangency, angle, or vector with magnitude, the splines tend to flatten out at the ends. Having the extra stations ahead and behind as I generate them, assures that the splines have fully developed curvature in the work area. The flattened ends will then be trimmed off before creating the surface.
First, just as an example however, I�m going to use the existing stations to create a surface to make a point. This is a surface generated, using the �Curve Mesh Surface� function in KeyCreator (your function may be called something different depending on program) I selected the stations in sequence as my primary curves, and used waterlines as my secondary curves.
We can see from the splotchy highlights on the turn of the bilge, that things are pretty lumpy. The causes are two-fold. The first is that the stations themselves have errors, either by the offsets not being transcribed properly, or by not having been properly faired to begin with. Being off by an inch won�t show on a �� to the foot hand drawing, but will get magnified by a computer. Another cause, is by the waterlines themselves. They force panels on the aft bottom, and forward sheer to be overly large , this causes crushing, and ultimately warping, of the surface flow lines at the opposing ends.
And now, were going to correct both.
Going back to the fore-and-aft view, I�ve laid in where I intend to create my diagonals. I�ve drawn these lines on the fore-aft view, at the midships plane.
Some notes on choosing how to place your diagonals: Looking at the screenshot, you will notice that they are not evenly spaced. As a general rule of thumb, you want your diagonals more closely spaced where the hull curvature is tighter. In this case, the turn of the bilge at midships is relatively even. Thus, I want my diagonals to intersect them at relatively even intervals along their length. At the forward stations, the upper flare is relatively slack, so the spacing increases. Down low where the curve is tighter, the spacing gets a little closer.
The second thing to consider, when choosing their placement and angle, is their normalcy to the shell plating. I.E. they want to be relatively perpendicular to the stations that they pass through. Notice that diagonals 2 and 3 in the above screen shot are almost perpendicular to all the stations they pass through. This is not always possible in all cases, however, so then the trick is to choose a diagonal that sort-of averages out, such as 1 and 5. In hind sight, I should have made the inboard ends of 6 and 7 a little higher to get a better average in this area, where there is a lot of twist. Luckily, there is a little room for error in this regard, and this surface should still work out OK as we will see.
The next step is to create points on the stations, at their respective depths, where they intersect these diagonals. In my case it�s done with �create point� -�intersection�-�at depth� and then selecting second if I selected the station second, or visa-versa. And I get something like this.
This next view shows how it all looks from the lower bow.
To be continued..
