STEMS

The meeting line fore and aft of the side panels of a Double-ender is not just a curved line; the angle between the panels varies from the sheer diminishing downward to the heel of the stem.  Its Profile view is shown in figure 3-1.  It makes construction of stems difficult for a new amateur who has only beginners luck on his side.

Fig. 3 - 1   The curved stem has a varying crosscut angle.

The degree of variation over the whole stem can be easily calculated, but it is a waste of time and effort unless you insist on a curved stem.

Side Panel Modification

From station #2 forward, and from station #14 toward aft, the side panels are no longer bent, but are allowed to continue in a straight direction as tangents to the sheer line circle segment.

Instead of coming together at station #0, the sheer lines join each other five inches fore of station #0 at the location #0-5", and aft at station #16+5".  This increases the Overall Length of the hull to LOA = 16', 10".

The angle that the tangent lines make with the centerline is equal to the bevel angle of cross frame #2 (and #14), which is equal to the angle of the center point angle between the radii R2 and R8 (= the angle between R14 and R8).  That angle is 22.24 degrees.  See figure 3-2.

Fig. 3 - 2   Side panels tangent line

Allowing the side panel to continue as the tangent line to the sheer line arc delivers two important simplifications:

1.         The stem becomes straight.

2.         The bevel angle of the stem, called the crosscut angle becomes constant.

What was the most difficult part to construct becomes one of the easiest to cut, especially for the beginning amateur with limited, or no carpenter’s skills at all.

SAC (Stem At Chine)

In figure 3-3, the Body view, the (maximum) bottom rocker between Beam and the heel of the stems is three inches.  The location where the two chine lines join the heel of the stem I call Stem At Chine.  For easy writing, abbreviated to SAC.  The location of Station SAC on the centerline is between stations #1 and #2.  See figure 3-1.  On the sheer line in the half-Body view of figure 3-3 that location is 

hsac = 22 x sin 22.62º = 22 x 0.3846 = 8.46”.

The exact location on the centerline of the station line SAC in Profile and half Bread view can be calculated with the formula:

hSAC + (R - hBeam) = v(R2 - dsac2), or 8.46 + (190.23 - 26) = v(190.232 - dSAC2)  in which dSAC is the distance between station SAC and  station Beam (station #8).

Worked out, dSAC = 79.785", or the location of station SAC = station #1 + 4.215" as is shown in figure 3-1, and more detailed in figure 3-4.  In this illustration the original curved stem and the sheer line the Profile and half-Breadth view are drawn in red.

The exact length, and the rake angle of the modified stem in black lines are written in.  Also shown is how one half of the constant crosscut is determined in this to scale drawing.  When the drawing is made on one-inch-grid graph paper a high degree of accuracy is achieved, even if it is done on a one-quarter scale.  It makes the rest of the Profile and half-Breadth views redundant!  All the important values of the measurements are written in.

The mathematics is just Pythagoras and the basic trigonometric definitions of Sine, Cosine, and Tangent applied.  It is all junior high school stuff.  If a check of the accuracy of figures of these measurements gives you any difficulty, just send me an email for clarification.

Fig. 3 - 3   Half- Body view of the Double-Ender

In figure 3-4, one-half of the crosscut angle is 31 degrees.  A 2"x3" ripped diagonally gives two right-triangular slats.  The tangent of the angle between the hypotenuse/cut and the 2½"-long-leg side is 1½/2½" = 0.6.  The angle is exactly 31 degrees!  Place the two 2½" sides of the slats back to back.  Cut the rabbet groove.  Miter the stem at 46 degrees.  In The Netherlands, where I was born, they say:  “Even a toddler can do the washing.”  See figure 3-5.

With the modified sheer line, the straightened-out stem, the raked tomb stone, or transom board, the increase of the Overall Length, the added guardrails and their capping, varying flare and the quoting of the outside measurements, it becomes more difficult for the untrained eye to recognize the original Double-Ender design from which the hull is developed.  However, it is still there!  But the most important result is that even a person with two left hands can now build the simplified boat.

Fig. 3 - 4   Profile and Body view of the modified stem

Fig. 3 - 5   Stem made from diagonally ripped 2"x3"

Skiff

In a 12-ft Skiff the building of a hull is further simplified by replacing the difficult-to-make stem aft with an even easier-to-construct transom board.

A vertical transom board does not need any modification of the original sheer line circle arc.  The bevel angle of the board equals the center angle between the radii R12 and R8 (Beam).  The distance between station #12 and station #8 is d12 = 48".  The sine of the center point angle is Sin CP-angle = d12/R = 48/190.23 = 0.252326.  The center point angle is 14.6 degrees.  The tangent of that angle is: Tangent 14.6º = 0.26.  Make a right triangular template from a piece of scrap plywood.  The long leg is 10"; the short leg is 2.6".  Set the short leg on the table of the saw.  Adjust the blade against the hypotenuse.  Cut the bevel on the side of the transom.  I never bother to draw a transom, but take its measurements directly from the setup.  It is foolproof.

Raked Transom

Besides the fact that it makes the boat roomier, a raked transom improves the beauty of the lines of the hull.  If the rake places the top edge of the transom between the sheers at station #13, the sides of the transom board require the difficult-to-make varying bevel angle.  This difficulty is eliminated in the same way as with the stem fore:  From station #12 toward aft, the sides are allowed to go straight in the direction of the tangent to the sheer line circle arc at station #12.  The varying bevel of the side edges is now the same constant bevel of station #12 which is 14.6 degrees.  It adds at the most 1½" on each side at the width of the transom board between the sheer lines.  The width at the bottom at station #12 stays the same.  Especially with a raked transom, take measurements directly from the setup.

FLARE

With flare, the bottom half of the boat is narrower.  Resistance when going through the water is reduced, the boat is more stable when heeling, and the beauty of the lines of the boat is enhanced.

Modern built dories all have varying flare.  But “classic” Dories, and the original Double-Enders from which they were developed have constant flare.  Flare can vary between zero (0) degrees (no flare) to the maximum (Dory) flare.  A hull with no flare at all is very easy to construct, but they are slow, and, IMHO, look like overdue pregnant bathtubs.  They can also be dangerous when heeling.

When we speak of flare, we actually mean flare ratio.  In figure 3-3 the flare ratio is 6.25/15 = 0.416667.  The same ratio is shown in the right triangle of the sheer line/hypotenuse with the half-Breadth long leg and the Profile height short leg.  The ratio here is the same 10/24 = 0.416667.  In a constant flared hull the flare ratio is always

Profile height/half-Breadth.

In most of the designs of hard-chined hulls, the constant flare ratio lies between the ratios 6/24 = 0.25 minimally and 14/24 = 0.583333 maximally.  The flare angle lies between 14 degrees and 30 degrees.  The reason why the ratio 10/24 was worked out is that with a constant half-Breadth of 24", the number 10" is exactly in the middle of the series 6, 8, 10, 12, and 14 for the Profile height figures.  See the table at the end.

It is easy to understand that when you make your own boat, you have a lot of choices.  The ratio 6/24 provides a roomier cockpit on a wider bottom with less tenderness than the ratio 14/24 which produces a faster boat on a narrower bottom.

The choice is yours.  Your choice depends on what you want to do with the boat, where you are going to use it, and any other personal preferences that you may have.

Without a heavy load the Dory is very nimble.  Windage takes a big easy grip on the hull.  Good tracking is difficult without a skeg or keel.  The rowing position is awkward.  It requires either long oars, or the handles of the oars that are right under the chin of a crewmember of average size.  The same characteristics that made her an ideal fishing platform in the wide ocean become disadvantages for the purpose of leisure boating in less open waterways.

The first modification would have to be reducing of the width of the side panels to provide a wider bottom, and a roomier cockpit.  The second change has to be the attachment of a keel beam with a skeg.  This improves tracking.  Both modifications make rowing easier and make the boat more suitable for the installation of a centerboard in a box and the rigging for sailing.

One more remark about this:  Whatever the modifications over time, the flare angle of the original design can always be found at Beam.  Even in varying flare Dories and the Double-Enders from which they are developed.  See the Dory picture.

To stay on the subject:  Dories are designed as “fishing platforms”; sturdy boats that stayed afloat under nearly all circumstances.  Their high sides give support to a bending-over fisherman trying to grab the lines of the catch.  The boat can take a heavy load.  They are easily stacked aboard of the mother-ship/schooner.  The lack of a keel and a skeg let them drift gentle at the fishing lines.  The beauty of the hull lines was, IMHO, an accidental quality.

Local weather and water conditions account for the change of constant flare into varying flare. This gave more accent to the fine cod’s head; mackerel tail shape of the modern dories which is visible at the bottom.  The sheer line amidships did not change, but the side panels fore and aft were allowed to follow the straight tangent line.  The curve in the bow stem became less pronounced and is easier to make because it diminished the varying bevel of the stem.  So was the bevel of the sides of the tombstone.  With these small changes, the development of the Dory shape had reached the end of the line.  See the photograph of a new Lunenburg Dory beside The Dory Shop at the end of the wharf of that city.

The Dory flare angle is exactly 33.69 degrees, or 33º, 41', 24".  I picture the raised eyebrows and the big question marks in your eyes.  At first sight it looks likes an extremely odd figure.  In realty it makes as much sense, and it is as easy to construct as the 3", 4", and 5" carpenters triangle.  Make the long leg of a right triangular plate 3", and the short leg 2".  (Making the template legs 6", and 4" is easier).  The flare ratio of the Dory is 2/3 = 0.66667.  The angle between the hypotenuse and the 3" long leg is then exactly 33.69º = Dory flare angle.  The pronounced flare angle contributes strongly to the beauty of the Dory lines.  I have serious doubts if even Don Elliot is aware of this Dory characteristic.

If you are still not convinced:  Check the flare angle of the Beam cross frame of the official drawing of the Lovell Dory.

The flare ratio = 2/3 was a (unconscious?) stroke of genius.  It made the setting up of the frames for the “classic” constant flare extremely easy and accurate.  I have spoken with several professional Dory builders who were not aware of this characteristic.  The older ones had received an elementary school education only, or, forced by bad economic conditions, even less.  Sometimes, they were more real artists than simple boat-builders anyhow.

THE SYSTEM

In the first article of this series, it is shown that all other hard-chined, constant flared hull forms easily can be developed from the original drawing of the Double-Ender, and the formula: 

Tan Flare Angle = Profile height/half-Breadth.

Calculating the radius of the sheer line circle arc segment provided the key, and became the basis for determining all the other measurements of a hull.  With the printed tables found here, that information is at your fingertips.  No need to make the calculations yourself.

The first table provides the radius R for all the flare ratios from 1/24 up to the maximum Dory flare ratio 16/24.  The second table is the calculation of the locations of the station lines on the hypotenuse/ sheer line in the Body view for the most common flare ratios from 6/24 up to 14/24.  The use of the tables will save you a lot of time and effort.

Table of the Calculations of the radius R for the Different Flare Ratios

The mathematical equation for the radius R is:  2 x hBm x R = (½ LOA)2 + hBm2.

The underlined figures in the table are the measurements of the Double-Ender described in this chapter.  On the same side panel width, the flare ratio figures above the line make the bottom wider.  The figures below the line will make the bottom of the boat narrower.  This ratio table saves you the trouble of having to make the calculations yourself.

Offset Table of Profile Heights and Half-Breadths

In general, the designs of most constant-flared, hard-chined hulls have a flare ratio between 6/24 (¼) and 14/24 (7/12), or a flare angle between 14 (14.036) degrees and 30¼ (30.256) degrees.

With this in mind, the plotting table for the actual sheer line arc, and the offsets of the Profile heights, and the half Breadths at the different stations is a great time and labour saving tool.

The table is based on the sheer line circle segment of the 16-feet double-ender.  The Profile heights at Beam vary from 6 inches to 14 inches on a (constant) half-Breadth width of 24 inches.  It lists the Body view measurements of the hypotenuses hn of the sheer line circle arc at the stations #2 = #14, #4 = #12, #6 = #10, and station #8 (Beam).  ½ LOA = 96".  The distances dn are between each station and station #8 (Beam) 

All the measurement figures in the table are given in inches.

The mathematical equation is hn = v(R2 - dn2) - (R - hBm).

The underlined figures are the measurements of the Double-Ender model constructed in these articles.

The Flare Ratio Table on the preceding page, and the plotting table for the heights of the sheer line circle arc segment above, eliminate the need to make any calculations.  Plot the dimensions on one-inch-grid graph paper.  Draw the hull lines completely in Body view.  Instead of the 10" Profile height at Beam as found in these articles, change to the Profile height of your choice, which can be any number between 6 inches, and 14 inches.

If you want to build a bigger boat, based on an 18', or 24' Double-Ender, just increase the scale of all the measurements by the factor 1½, or 2.  It is that simple with this mathematical system of design.

SIDE PANELS

In the half-Body view of a Double-Ender, figure3-6A, the chine line is drawn parallel to the sheer line.  The side panels have the same width over the whole length.

The rocker from the Beam to the stems is 7.4".  Station BAC (Bow At Chine) has moved forward to station #1 + 0.655”.  The chine lines in Plan and half-Breadth view run parallel to the sheer lines.  This strong rocker is still visible in the McKenzie-River Dories.

Fig. 3 - 6   Chine lines parallel to the sheer lines

Cod’s Head, Mackerel Tail

In figure 3 -7A, the original chine lines parallel to the sheer lines are the dotted lines.  In this drawing a new chine line is drawn in red.  Instead of a rocker fore of Beam of 7.4", this rocker is reduced to 3", a difference of 4.4".

At the same time the rocker aft of Beam is increased by the same amount of 4.4”.

The bottom is no longer parallel to the (horizontal) plane of the two sheer lines, but tilted from fore to aft as shown in the Profile drawing of figure 3-7B.  Although the sheer line itself has not changed, the bow has become substantially higher. (or should I say the bottom fore deeper?)  In Dories this is not so pronounced as in the Punter, but still clearly visible in the photograph of the Dory in this posting.

Fig. 3 - 7   Cod’s Head, Mackerel Tail

Figure 3-7B shows how this modification changes the contour of the bottom/chine line.  Station BAC is now located at station #1 + 4.215".  This station has moved aft.  At the same time Station SAC moved over to station line #16.  The worked out formulas under the figures3-6A and 3-7A show exactly over what distance the movement took place.