Finishing Up the Guide Boat

    New oars on the left; old oars on the right.

My latest guide boat is essentially finished; just adding varnish.  I also built a new pair of oars for the new boat.  Using published formulas for proper oar length, standard oars would be about 80 inches long according to the boat beam, but I also read a note, "Guide boat oars are usually 7 1/2 or 8 feet long."  I have a fairly large stack of scrap wood which I need to use.  From the scrap pile, I found some nice straight pieces to bond together creating 92-inch long oars with the inboard ends left with a chunky square profile to help counter balance the somewhat longish outboard shafts and blades.  I am not going to go into oar construction because there are already plenty of Google instructions posted.

Taken on the US Air Force Academy.  We are still discovering more trails in the Colorado Springs area; although we also took the bikes to Arkansas and Montana this summer.  They are a great source of exercise and fresh air away from crowds of people (and COVID).  Building boats is more enjoyable when the weather turns cold.

I want to apologize for the slow progress in recent months.  Progress has been slow to non-existent during the better weather of Summer and Fall because my wife and my own infatuation with the new e-bikes we purchased.  With the mountain e-bikes we feel confident to go further and steeper on our outings than we would with regular bikes.  It has been a godsend letting us travel forest trails with fresh air, ample exercise, and no crowds.

The hull ends are symmetrical and the oarlocks are set about a foot ahead of the hull midpoint. When rowing with two people onboard, the rower sits ahead of the oars.  When rowing solo, the rower sits at the hull midpoint facing the other direction.

    Seat positioned amidships for a solo rower.  Yes, it is snowing outside.

Now that winter is here, I'll be looking for a project in my wood shop to keep me busy.  Still working at the clinic, but only 2-3 days per week.  My present thought is to build another guide boat using what I have learned building this one.  Always trying something new; I anticipate using a 14' length (more easily cartop-able) and a wider plank keel. I was able to buy a length of flat lumber 12'2" long and 10.3" wide. I'll see how the wider keel changes the hull stability. 

Finishing the planking

I put off making choices for planking.  Previously I have always used a plywood initial sheathing to define the surface shape and provide a substructure for bonding exterior thin planks; it works well with developable surfaces.  I had some marine plywood on hand.  Also had some  mahogany planks left over from my last build, but there was a reason they were left over.  The planks had flaws; they were the rejects.  This new boat is somewhat of an experiment; didn't want to invest too much in materials; so I used those rejects.  And I have been reminded how important it is to keep focused and not compromise at any step.  Later on it catches up with you.

Now I am doing extra sanding and using fairing putty to make up for those inferior materials used.  Next time I will spend more time and money to produce high quality planking at the very beginning.  Even the garboard would be better with solid planking than the altered four-ply plywood I used.  I would also omit two of the intermediate stringers in the frame work; they have not added much to define the build.  A stringer at the initial chine and at the sheer would be enough framework. 

 

Getting to the final touches.  Need to finish all the trim, build some seating, and create oars.  I painted the interior because the planking is not uniform; thus, not all that visually appealing.

Creating a Developable Surface

This has nothing to do with any computer program and its underlying algorithms; instead, let's consider basic geometry, some algebra, a touch of trigonometry, and perhaps some optional calculus.  Developable surfaces cannot include curvature in multiple directions at a single point.  A straight line must pass through any point on such a surface; these are called "ruling lines".  A unique line can be defined by either two distinct points in space, or one point and a defined slope.  Surfaces can be created by projection from points: parallel in two dimensions (flat), parallel in three dimensions (think of a cylinder), or conic- radiating from a single point which I will call the focus or focal point (FP).  Multiple projections can be connected to create a fair surface as long as those projections are linked by common ruling lines.

 In this sketch of the topsides of a previous boat, I used four projections. I used a parallel entry for only a short distance.  Then I switched to a conic projection (using a common ruling line) to create a flaring bow.  Next, I moved to a different conic projection for a transition to stern tumblehome.  Finally, a parallel projection was used to finish the tumblehome.  You can see how projections are combined, using common ruling lines, to create varied surfaces and the desired shape.  All projections were done from defined coordinates along the chine or extensions of the chine.

First, let's concentrate on ruling lines.  On a segment of any line between two points in an X-Y-Z-defined space, the change in X is proportional to the change in Y and the change in Z according to the slope of the line.  The slope can be calculated as (X1-X2)/(Y1-Y2)/(Z1-Z2) if we know the coordinates of two points on the line.  We can calculate the coordinates of another point (or multiple points) on that line (X3,Y3,Z3) using (X1,Y1,Z1), the calculated slope, and any one of the X,Y,or Z coordinates for point 3.  Let's assume we know X3, then the formula for Y3 would be the following:

Y3= Y1-(X1-X3)(Y1-Y2)/X1-X2)
Z3= Z1+ (X1-X3)(Z1-Z3)/(X1-X3)

In words, the change in Y is proportional to the change in X, and that change is then subtracted (or added, depending on direction) from the initial Y value.

Here comes the big concept which makes this whole system work:  In order to make this work, we need some defined points in virtual space to start describing our desired surface.  We can't just draw a line on paper and say that this defines one edge of our surface.  We need numerically exact discrete points.  A mathematically defined curve provides the solution.  I generally use a form of trajectory curve, also called a parabolic curve, for this purpose.  An example below:

Y=14.4-(72-X3)squared (14.4) /5184          (5184=72 squared)

Z= 4.8+(72-X3)squared (5.76)/5184

The X-Y slope at any point =2(14.4-Y3)/(72-X3) where X is measured from the bow and Y from the midline

If you integrate the curve (which I will not do here), you can calculate the length of the curve or a section of it.  I actually did the integration calculations for the hull I am building.  It eliminated the need for a strongback frame as the parts were self-aligning. 

Using these particular curves, I insert values of X3=66,60,54,48,.... etc. and solve for Y and Z values at each of these X intercepts.  This provides a table of exact coordinates, spaced every six inches along a chine curve.  I could calculate values every three inches if needed, but the extra accuracy is unneeded.

Let's say I am designing a guide boat with a frame every 12 inches (which I did).  We have the chine; what should the bottom look like?  Displacement, stability, and construction considerations help decide this.  I decided on a midships deadrise slope of  1:3 and a plank keel 7.2 inches wide (can use standard 1x8 lumber).  Now for the projection.....

By setting Y=0  (width=0), we can solve for X and Z (length and height) and plot the bow profile.  Note that as the focal point (FP) is located nearer to the surface being described, the resulting projected curvature increases.  This is generally true.  Note also that the ratio of Y to Z at the FP is the same as the midships deadrise, z/y=1:3.  This has to be true to create a common ruling line.  Shifting the X coordinate fore or aft also affects the slope.  If the corresponding X coordinate matches the stem half angle (defined as Y/X), it will create a plumb bow.  (Y/Z ratio is fixed by the midships deadrise ratio.)    

By setting Z=1.2, we can solve for X and Y (length and width) and create the plank keel profile with a width of 7.2 inches.  Using a conic projection results in a longer keel with slightly more abrupt entry profile.  

We have a choice of projections for creating the frames at X=,12,24,36, etc.  This drawing was created using a projected parallel profile, X:Y:Z= 6:2.4:0.8.

These frame profiles were created using a conic projection.  The FP is located at (-20,-9,-3).  Recent experience suggests that the conic projection may be superior in this application; it depends on what characteristics you value most.  A conic projection appears to shift some of the surface curvature near the stem from the Y-Z plane to the X-Y plane.  At least that is my current best guess.  The parallel projection creates a more aesthetic bow profile curvature, but a shorter waterline length.

Posted to answer a question asked:

 

Demonstrating the alignment of frames using the plank keel, and the calculated length chine and sheer as references.  These pieces will only fit together in one relationship when aligned.  No strongback needed.

Because this hull is designed as a developable surface, compound curvatures are avoided when planking.  By using a triple chine design (not including the plank keel edge), plus narrow planking (2" wide), the result closely simulates a rounded, non-developable shape.

   

Solving the hull sheathing conformation

Spring is here but Pikes Peak still is snow covered.

Wow! Has it been so long since posting previously?  Over six months?  That has been time for three vacation trips and a major bathroom renovation.  It is nice to stay busy.  Now with the pandemic, things have slowed down some, and it's back to the guideboat project.

In the back of my mind has been that failure of the garboard sheathing to conform to my design dimensions.  The plywood when bending aligned itself with a different curvature, lower stress pattern.  Today, I did a simple investigation.  By laying a straight edge (I used a four-foot level) on the hull sheathing and rotating around a tangent point it until the entire edge contacted the surface, I was able to discern some of the actual (approximate) ruling lines inherent in any developable surface.  I had designed the hull bottom to be a parallel projection; the X:Y:Z ratio was 6/2.4/-0.8.  It appears that, instead, the plywood adopted a conic projection toward the hull end.

Ruling lines marked on the sheathing plywood.

I marked some of the ruling lines on the hull surface.  As you sequentially view the ruling lines from midships toward the ends, The first line is consistent with the design slope.  The second line converges with the first line toward the hull midline.  Converging lines indicates a conic focal point in that area.  Subsequent ruling lines at the hull ends only slightly converge but with steepening deadrise (Y/Z slope).  Looking at these lines and viewing the hull surface from various angles suggests to me a conic projection, or several conic projections, with focal points located forward and across the midline (keel).  On my previous guide boat design, I had used a conic projection in that area.  I used a parallel projection on this hull, expecting that it would be superior, and it is for general purposes.

Initial convergence toward the keel of the ruling lines from midships proceeding toward the ends.

Slight convergence with increasing deadrise for marked ruling lines.

I think I have solved this puzzle.  The plywood was thin enough, and with only a four-ply unbalanced stress resistance, to relieve stress by distorting slightly at each of the frames creating an unpredictable conformation with a lower induced-bending-strain pattern; at least in this situation of a long, comparatively slender hull panel.  I will make sure that I never face this situation again.  I want predictability; not repetitive cut and fit construction.