Station #13
The plans are not exactly clear about how to finish off the last 6 inches of the keel located between Stations #13 and #14. While the plans specify the 5+5/8" and 4+5/8" horizontal offsets for the top and bottom corners of the back edge of the plank, the plans do nothing to locate the corners vertically. And what are we to make of the magic floating 3" measurement?
Original Plans:
In trying to replicate the drawing around station #13, it is reasonable to assume that the angles between the top and bottom edges of the keel and the reference line near the stern should be constant. The top edge of the keel rises 11/16" from Station #11 to #12, and another 11/16" to reach Station #13. That looks pretty constant to me, and would give the boat a flat run at the stern, which is ideal for hull speed. It also straightens the last 30" of the top of the keel, which facilitates measuring that 112° between the transom and the keel. So the top corner of the keel should be (5+5/8")/(12")*(11/16") ~= 5/16" higher than it was at Station #13, or 3+11/16" above the reference line. For the bottom edge, if we continue the slope from Station #12 through #13 and onward for another 4+5/8", we end up with the bottom corner (4+5/8")/(12")*(1+5/8") ~= 11/16" higher, or 1+3/16" above the reference line. Now our drawing would look like this ...
Replicated:
Clearly something is amiss. The angle from the top of the keel to the transom is now 115°, which is much larger than the 112° specified elsewhere in the plans, and the deck will not be long enough to fill the gap between the stem and the transom. The angle of the run (top of the keel) with respect to our horizontal reference line is arctan( (11/16")/(12") ) = 3.28°. If we subtract 3.28° from 112°, our target angle from the reference line to the transom at the rear of the keel becomes 108.72°.
So what could that magic floating 3" be referencing? How about the vertical distance between the top and bottom corners of the keel? The horizontal distance between the corners is 5+5/8" - 4+5/8" = 1". A vertical rise of 3" with that 1" horizontal run specifies an angle of arctan(3"/1") = 108.4° , which is very close to our target of 108.7°. Keeping the 4+5/8" horizontal dimension of the rear corner constant and sliding the corner downwards to 3/16" to achieve that 3" vertical separation, we arrive at this configuration .
Adjusted:
But now we have a rather rude kink in the bottom of the keel. Looking carefully at the offsets and doing a little math, we discover that the angles at the bottom of the keel from Station #6 rearward are 1.9°, 3.9°, 5.4°, 5.4°, 6°, 6°, 7.7°, and 1.6°. Clearly the 7.7° angle at Station #13 is too steep. If we lower that point from 1/2" above the reference line down to 1/8", the angles become 1.9°, 3.9°, 5.4°, 5.4°, 6°, 6°, 6°, and 6.2°. Much better. Also, we can adjust the bottom corner by 1/16" down and forward to get the transom angle closer to a whole degree, which will make the measuring a little easier and more accurate. So it appears that the plans should have been drawn thusly .
Corrected:
But now the plans are a little cluttered. The two important details are that the top corner be located 5+5/8" rearward of Station #13, and that the transom rise upwards from the reference line at 109°. So we can delete all of the extraneous information from the plans and redraw them thusly ...
Simplified:
... and then add the explanation that the batten marking the bottom of the keel should run long to complete the curve of the bottom and locate the corner where it meets the 109° of the transom.
Conclusion:
We can summarize these alterations to the plans thusly.
- At Station #13, the bottom edge should be lowered from 1/2" above the reference line to 1/8" above the reference line.
- The top rear corner of the keel is located 5+5/8" beyond Station #13, and 3+11/16" above the reference line.
- The bottom rear corner of the keel is located about 4+9/16" beyond Station #13, and about 5/8" above the reference line.
- The rear edge of the keel should be angled 109° from the reference line, should pass directly through the top corner, and pass within a nail's diameter of the where the bottom corner is marked.
Clarified 1980's Version:
