Driveway shots
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Periodically, I drag the boat out of the garage and into the sunshine to check on my progress in the bright sunlight. This also affords the opportunity to clean the garage of saw dust and wood scraps.
Attaching the hull bottom to the keel makes the hull truly 3-D.
Up until this point I have been making do with a very simple cradle made from 2 by 4 stock. The base cross member is laid flat with wheels screwed to the bottom. A pair of braced uprights are spaced 1/16th of an inch wider than the keel on the center of the cross member. The weight of the boat bends the flat cross member ever so slightly which causes the uprights to pinch together and grab tightly onto the keel.
Now that the transom, bulkheads, and deck have been attached, I have to seriously start thinking about building a proper cradle.
The plans warn that as the work on the boat progresses, small sizing errors in the individual parts can accumulate and become noticeable. Therefore, later in the construction process, the dimensions noted in the plans should be used as a guide and adjusted as necessary from actual measurements from the boat itself. However, I was noticing differences right away.
If you look closely at the photos on the right, a small one inch gap should be visible at the front of the slot where the foredeck meets the stem. So either my keel is one inch too long, or my deck is one inch too short?
The deck is made from three pieces of plywood; a foredeck of 4'7", side-decks of 8'0", and a cockpit of 3'2 ½", which total 189 and ½ inches and is what my deck actually measures from stem to stern. So I must have erred earlier in the process somehow ending up with a keel assembly that is one inch too long. I would guess that the error is in the transom to keel angle with the transom leaning too much resulting in a larger gap from stem to stern than is indicated on the plans.
The plans indicate a 112 degree angle between the top edge of the rear of the keel and the deadwood that supports the transom. But the top edge of the keel is a slowly flattening curve and it matters how you measure that angle. Different sized protractors or angle keepers with legs of different lengths will measure that angle differently as the tip of the lower legs land progressively further out along that curve.
If we apply a little bit of Euclidian Geometry to the plans, we might discover what went wrong and ensure that the plans as drawn are accurate. Using the top edge of the original plank the keel was cut from as a horizontal reference, we can calculate the horizontal distance required for each part of the keel assembly by multiplying the cosine of the inclination angle of the part by the length of the part. For example the back edge of the stem is 37.5" as per the plans and rises at an angle of 50 degrees from the reference line, so 37.5"cos(50º)=24.1". The slot at the stem is 6.75 inches long and is inclined by the complement of 39º from that 50º, so 6.75"cos(180 º-50 º+39 º)=6.63". The stem falls 1 inch forward of station line #1. The distance from station line #1 to the end of the keel is 12 feet 5.375 inches.
Which brings us the deadwood at the stern. The rise along the top from Station #11 to Station #12, and then on Station #13 is a constant 11/16 inches per foot, which works out to the arctan(3.688/12) = 3 ¼ degrees. So it would be reasonable to assume that this is the edge from which we are supposed to measure our 112 degree angle from to locate the transom. But to continue with our calculations we really want to measure from our reference line, so 112 degrees - 3 ¼ = 108+3/4 degrees from our reference line. Continuing, the transom is 20.5 inches tall at 108+3/4 degrees, or 20.5"cos(108.75 º)=9.93". Adding it all together 6.626" + 24.105" + 1" + 149.625" + 6.951" and then subtracting out the 3/8" thickness of the transom totals 187.932 inches of horizontal distance, which is less than the 189.5 inch length of the flat deck assembly. So far, so good.
The deck is installed at an inclined angle with the stem higher than the stern so we have to inflate our horizontal distance by the cosine of the angle of inclination. We need to know the vertical separation between the front of the slot and the top of the transom. Working with the same part lengths and multiplying by the sines of the inclined angles yields 6.75"sin(169º) + 37.5"cos(50º) - 20.5"sin(108.75 º) = 11.08" vertical separation. Rise over run is one of the definitions of the tangent of an angle so we can finish our calculation as 187.932"/cos(arctan(11.08"/187.932")) = 188.252", which is closer to but not equal to our 189.5" deck length.
But the deck doesn't span the distance from stem to stern in a straight line. Instead, it sags like a catenary, curving down from the stem to the front bulkhead, across to the cabin bulkhead, and back up to the transom. We can approximate the catenary with three line segments of lengths 54.77", 66.31", and 67.73 that follow the same path and add up to 188.81 inches. Closer still, but not exact.
I was going to parameterize the general formula for the catenary function f(x,k)=cosh( k*x) to fit the curve of the deck, from which we could compute the integral of the derivative of the above hyperbolic cosine, which is f sinh(k*x)*k, when it dawned on me that I could simply measure the sag directly on the boat I had already built. Measurements of the length of the deck with a cloth tape measure alternately stretched very tightly in a straight line from slot to transom, and then relaxed enough to allow to tape to sag and follow the curve of the deck, resulted in a difference of 7/8 ths inches. Flat deck length of 189.5" - 7/8" catenary sag = 188.625" length of curved deck, which is .375" longer than our 188.252" calculated inclined deck length. So the plans are a little off.
Stock Plans:
If we increase the reference line to transom angle from 108.75 degrees to 109.75 degrees, then the plans are correct to with 9 thousandths of an inch.
Modified plans:
But none of that explains what happened to my boat. The plans show a 112 degree angle that Euclid says is 1 degree too tight, which should result in a boat where the deck is 3/8" too long to fit into the slot. Mine has a 1 inch gap, which is about 4 times that distance in the other direction, or equivalent to an excess of almost 4 degrees, or a 116 degree angle from transom to keel. If I place my fancy adjustable square with its integrated protractor right on the transom to keel angle, as built it measures exactly 112 degrees. The Stem to keel angle is exactly 50 degrees, the stem 37 ½" long, the slot is 6+3/4". And yet there is a one inch gap at the front of the slot. Maybe the keel is an inch longer than it should be? It's a little hard to measure the keel sitting in the cradle, so this final check will have to wait until the boat gets flipped for fiberglassing.
In the mean time, I just cut a template from 1/8" masonite for the front half of the hull side skins, and sure enough the slanted angle where the sides meet the stem is a little askew. If I move the bottom front corner forwards by an inch and re-cut, the template fits perfectly. This is consistent with the deck being positioned 1 inch too far back with respect to the stem and hull bottom.