By Rob Rohde-Szudy - Madison, Wisconsin - USA

Measuring & Drawing Hulls - Part 2

To Part One

…and a new design!

Last month we measured an instant boat hull and drew. Now we’re going to use common spreadsheet software to help detect and correct our errors.

Spreadsheet graphing

Let’s start by entering our measurements in the offsets table. There is no one right way to set up an offsets table, so do what suits you. However, I do recommend using bold print for measurements taken from the actual hull, and plain text for those taken from the drawing. We will assume the latter to be +/- 1/4”, as mentioned above.

If we use spreadsheet software, we can use the graphing functions to double check our work. I use a scatter plot, as this plots x,y coordinates so we can see if the line is actually fair.

Note that in MSExcel you can format each data series to make a “smoothed line” between the points.

The scales are not equivalent to the actual boat, but because the curve looks fair, everything is probably in order. Actually, it is easier to see something out of order when you intentionally distort the scale.

This reveals a couple things. First, at the far right I have two points on the transom that are the same distance from the stem (see arrow). They shouldn’t be. This was a data entry error. The coaming distance from stem should actually be 187 inches. It still jumps out of line, we’ll fix that in a minute.

The other arrow notes some points that are kinked out of line. Here we need to decide which points are more likely to be correct. If any of these were measurements directly from the hull, I would favor those. However these are all from the drafting, so we are several layers of potential error from the real thing. However in this case I notice that my rubrail point is kinked in on the same station where my chine is kinked out. I think I probably made a bad measurement on that station. Tweaking those half breadths unkinked things. I also added the missing point on the chine and made a few other more minor adjustments, since this foreshortened view reveals more errors than the actual drafting.

Let’s look at the updated profile with the other two views and make sure we didn’t screw anything up there. It is best to check this after every change.

Except for a very slight kink in the cabintop, the stern is our only remaining problem. The three lines on the transom should be colinear in all three views, which is currently not the case in any view. So what are we surest of? The length to the transom top and bottom were measured from the actual boat, as was the transom height and transom bottom width.

I think we can be pretty sure I have the distance from stem a little long for the rubrail. Changing that and moving it slightly outboard seems to get things in line. But since we’re doing math, why not check all of the lines that should be straight?

Checking for colinearity with slopes

The side of each bulkhead, the stem and the transom should be straight, which means all points that fall on them should fall on the same line. We can check for this mathematically.

This is actually pretty easy since we’re dealing with known points. All we need is slope, which is rise over run. (Divide the change in height between two points by the change in half breadth between two points.)

I do this by figuring the slope of the line formed by the point on the chine and the point on the cabintop. Then figure the slope of the line formed by the point on the chine and the point on the rubrail for the same station. Since they start with the same point, all the points are on the same line if the slopes are the same.

The transom is a little trickier, since we need to whip out the Pythagorean theorem to come up with an accurate “run” figure. I also added a “flat slope” for the transom to make sure the rubrail and coaming lines (from chine) have the same slope as viewed from above. Here is the table of offsets with slopes added at the bottom.

Yikes, these are all over! Actually they are not as bad as they look, but the transom is still noticeably off. The flat slope is looking good (and it does on the plan view), but we’re still not in line. Let’s look for patterns.

Notice that the differences between the rubrail and coaming are all in the same direction except the one at BH2. I have a lot more confidence in the curve I drew for the rubrail, because it is a nice, easy curve. For that coaming I had to fight the spline to keep it on the page without nailing it down. At BH2 and changed the coaming half breadth only 1/8” and the slopes match close enough to leave it. This is well within the expected error for drafting. One station aft of BH2 I had to move the point 1/2” inward. This is a bigger change, but still quite believable, given my struggle with the spline. Moving aft I changed stations by 1/4”, 1/8”, and 1/8”.

This brings us to BH3. Here I believe the actual measurement from the boat on the coaming more than I believe my drafting measurement on the rubrail. It only took a 1/8” change to fix it, but this necessitated a 1/8” adjustment to the station forward of that to re-fair the line. This didn’t affect my modification of the coaming, but it could have.

Back to adjusting the coaming, a 1/8” adjustment of the station aft of BH3 does the trick.

This brings us to the transom, which is seriously messed up. What I call “flat slope” is the transom edge angle as viewed from above. This is in pretty good shape. But the slope along that line is not good at all. The problem is in the “side slope” component. The measurement I’m least confident in here is the distance from stem at the rubrail. I had to move this a full inch to get it right. I suspect this means I counted wrong when writing down the measurement from the drawing.

Here’s where we stand:

Boy, that sure got kinked up in the plan view. We also have a noticeable unfairness in the profile. Let’s fix that first and see if it fixes the plan view. It did, and it only took 1/8” of adjustment in both height and half breadth.

Obviously we still have issues at the stern. Our slopes at the transom look great, but I know I didn’t kink any wood that tight. That kink would require steam or many more laminated layers than the three I used. Again we look for what we doubt the most. At the station between BH3 and the transom nothing was measured from the actual boat, so let’s see what we can do. The biggest kink is in half breadth of the coaming. It is fixed by adjusting the coaming 1/8” in half breadth and 1/4” in height.

Now we have a much improved offsets table, and any bulkheads made from it should be considerably more accurate.

Onward Toward a New Design

Now we get to the reason I started this whole measurement process. After spending a season with my made-over AF4B, I finally knew what I needed to do to have my idea of the ideal small family powerboat. I needed only a small cabin for the potty and for hanging up life jackets and other things that should stay dry. Maybe for kids to nap in occasionally. I especially needed a bigger bow well for both kids to ride up there together. Even doing both of these things I could still squeeze out a bigger cockpit, which is where all the grown-ups always want to be.

I’ll have more detail later on how this worked out, but for now we need some dimensions for new bulkheads. How do we do it?

New Bulkheads

First we need to know the fore and aft position of these bulkheads. Then we make lines perpendicular to the baseline at these positions on the profile/plan view. In this case I wanted them 3.5 and 7 feet aft of zero (top forward corner of planking). We already have a section line at 7, so we draw in 3.5.

This provides us the height on the profile view and the half breadths on the plan view. We transfer these to the section view.

Knowing this we can draw the shape of our new pieces of plywood.

But we’re not done. We still need to know the…


Michalak discusses how to figure bevels in his articles on hull design. But Jim is a real engineer and his method for calculating bevels reflects that. For him, advanced math like cross products and matrix multiplication are a pleasant stroll down memory lane. For most of us they are excruciating mental exercise to remember or learn. In my case it was learning—I can assure you that they don’t teach that stuff to music majors.

Of course it was after I bothered to learn all that math that I discovered a far simpler way. You can do it right on the plans if you have a section view. (If you have a table of offsets, you can draw one.) Best of all, it works exactly the same as Jim’s method. It’s just graphic rather than mathematical.

First we need a line at right angles to our bevel line, which also connects to the next station line. Let’s call its length on the section view a. This line should be the same length no matter where you put it on that bulkhead, since the lines defining the sides should be parallel at each station. (If they’re not you can’t rip constant-angle bevels!) I didn’t even draw the line. I just lined up the scale rule and squared it up with the drafting triangle – I’m measuring about 2.25” starting at zero on the scale rule. (I removed the triangle to make the photo clearer.)

Easy, right? Well, if our bulkhead is square athwartships and plumb, that tells us all we need to know. The other part we need is the distance from our bulkhead to the station that contains the point that a connects to. The plan or profile view will have this. Let’s call it b. In this case it’s the 6” between our new bulkhead at 3.5 and the station line at 3.

Now we draw a triangle. A draftsman would project it right on the plans, but I do it on separate paper to keep the plans cleaner. First make a line and mark off the length b. At right angles to one of the ends of b, mark the length a.

Then connect the unused ends of a and b. The acute angle is your bevel angle! I extend the lines to make it easier to measure with a protractor.

There’s no reason to draw separate angles as long as the station spacing stays the same. Just mark off new lengths for a and fill in the angle line.

These results let us put bevel angles on the bulkhead drawings.

You can actually do the same thing for rolling bevels too. You just need to use this method figure the bevel angle at both the sheer and chine. Then after making some initial cuts on the bulkhead’s framing stick, you strike a line between the two cuts and do some careful planing to finish it. Fortunately, we don’t need to go to the trouble with untwisted instant boats.

If you don’t want to mess with the protractor, you can calculate the angle from the lengths of a and b. Pythagoreas can help you out with something you might remember from high school trigonometry. The figures we know are side opposite and side adjacent of a right triangle. Tangent is the ratio of the former divided by the latter. To turn tangent into an angle, we calculate its arctangent. In spreadsheet software like MSExcel this looks like “=degrees(atan(a/b))”. If you refer to other cells for the variables, this can be very quick indeed.

So now you tall guys know how to refigure the bevels when you need to move a bulkhead to be able to sleep in your cabin without contortions. Or how to reduce a cabin to a cuddy.

Checking Measurements

Let’s fit some real bulkheads! I made cardboard patterns, since it doesn’t pay to trust anyone’s draftsmanship at 1/12 scale for an exact fit. My fine pencil line is at best the equivalent of 1/8” wide, after all. Surprisingly, the front bulkhead at 3.5 fits perfectly!

But bulkhead 7 leaves a gap at the top of each side.

This means we had better double-check some measurements. As it turns out my measurement at the top of the aft cabin bulkhead was wrong. This is a lot easier to see after the cabin top is cut off. I guess I should have measured with sticks instead of a tape measure, but I this is at least partly the result of a small inaccuracy in the original hull. See how these cabin top stringers bulge out unfairly?

Here’s why. There’s an unsupported butt joint.

With this in mind I did not redraw the plans using this “corrected” measurement, since I think the splined lines are closer to what the hull is supposed to be.

I should also point out that it is best to consult the designer before attempting to move bulkheads around. But I guess I’m a designer now that this boat has evolved this far.

A new design – Sandy Shoal 16

Complete plans are available through the Duckworks store, and I’ll be telling you more about this design next month.

Rob Rohde-Szudy
Mazomanie, Wisconsin, USA


Click Here for a List of Articles and Columns by Rob Rohde-Szudy

To comment on Duckworks articles, please visit our forum