Boat Building Plans And Kits | Sample Developable Design calculations

Boat Building Plans And Kits

In 2008 I wrote a short paper on a mathematical method of developable hull design (which is included in this blog, see entry of Dec. 2008).  I tried to keep it short and discuss only general principles, but some subjects are difficult to understand without providing examples.  Without any examples, I dont think it was very meaningful for most readers.  Recently the subject came up again, concerning the difficulty of developable design and the paucity of explanatory material.  Last night, I wrote a short paper concerning a stepwise approach and actual sample calculations involved in creating a hull shape.  The numbers used are from the runabout building in my shop currently.  The paper is not a comprehensive "how to" but hopefully will make the subject more easily understandable.

Sample computations for Developable Design

To illustrate the generation of many exact points along the chine curve, the following is a list of some coordinates of the chine at 7” intervals for the anterior chine of the hull I am now building:  (0, 0, 24.48), (7, 3.2, 22.56), (14, 6.3, 20.7), (21 ,9.2, 18.96), (28, 11.9, 17.34), (35, 14.4, 15.84), (42, 16.7, 14.46) ,.…. until (119, 28.8, 7.2).  This series is generated from the parabolic curve Y = 28.8- (119- X)squared / 490 and also Z = 0.6(28.8-Y) + 7.2 and is valid for values of X between 7 and 119. 

Where did these equations come from?  I want a boat about 6’ by 18’, so I picked a length of about half that which I could evenly divide into 16 segments [more segments = more accuracy]; 16x7 or 112” will suffice, next add a short straight 7” segment onto that.  Have you ever noticed that when you bend a batten, the curve does not extend all the way to the end of the board?  At the batten end there is no fulcrum to apply torque.  Thus, last few inches have no bend unless confined along its entire length.  So I always add a straight segment at the end of every curve.  A 6’ beam gives a 36” half beam; minus some width for flare of the topsides (4”) and an allowance for a chine flat (3.2” at maximum point) and you end up with 28.8” chine beam which is 25.6” of camber in the 112” length and 3.2” of offset along the 7” straight end segment.

To create the forward keel projection, I most frequently use a parallel projection.  A conic projection, with the apex of the cone forward, will create sharp curvatures in that area.  It may be what you want, but it will also be hard to plank.  A conic apex amidships will give a mild curve at the keel, if that is what is desired.  The parallel projection has a controllable curvature and is easy to calculate.  We already have defined a 28.8” chine beam, and picked a 7.2” deadrise to go with it [based on estimated displacement].  So deciding on the slope for this parallel projection from chine to keel only involves selecting an X intercept from the maximum chine point (119, 28.8, 7.2).  The further forward we select this point, the more pronounced will be the forefoot of the keel with sharper curvature.  I chose a point 52.5” forward of maximum chine beam.  52.5/7.5 = 7; 28.8/7.5 = 3.84; 7.2/7.5 = 0.96; thus we have our slope, X: Y: Z=7: 3.84: 0.96 which coincides with the 7” segment intervals.

Now all anterior keel intercepts can be calculated to define the keel.  At the keel, Y=0, and we solve for X and Z.  X@keel= X@chine- (7/3.84)Y@chine and Z@keel= Z@chine– (0.96/3.84)Y@chine. Aft of the point X=119”, the keel is straight and Y=0 & Z=0 for the keel.  After finding the shape of the keel, we next move on to the shape of the transverse frames below the chine.  To calculate transverse frame shapes below the chine, the same slope or ratio is used.  We set X = 14, 28, 42, etc., or whatever other frame locations desired, and solve for Y and Z.  For every 7” forward we project a chine coordinate, the Y dimension will decrease by 3.84” and the Z dimension will decrease by 0.96”.  Simple math creates the entire shape of each frame.  Just connect the dots.

Creating topsides with some flare to the bow, transitioning into a tumblehome stern, seems to be best accomplished with a conic projection forward, linked to another conic apex further aft to create the transition, then a parallel projection extending aft to finish the tumblehome contour.  Conic projections involve finding a third point on a line give two defined points.  Rather than discuss an entire design, I will list selected apices and show sample calculations.

The apex of the first cone was selected at X, Y, Z = (56, 39, 70.2).  This will give a bow angle which matches the forefoot of the keel and provide moderate flare to the topsides not to exceed a 6’ total beam.  A sample calculation would be to calculate the Y and Z intercepts at the frame location X = 98 for a line between the apex and the chine coordinates (119, 31.9, 7.2).  The calculation is Y = 39– (98- 56) (39– 31.9)/ (119– 56) = 34.27 and Z = 70.2– (98– 56) (70.2– 7.2)/ (119- 56)= 28.2.  The relation is that the change in any one coordinate of a point on a line is proportional to the change in any other coordinate.  Since we choose our X intervals, we can then find Y and Z.

When calculations are complete for X between 0 and 126, we select a second apex (91, 35.5, 38.7) which lies on the ruling line, halfway between the first apex and the point of maximum chine beam (to the outside of the chine flat) which is (126, 32, 7.2).  This new apex is then used to calculate points aft to the chine location (189, 32, 7.2).  From there a parallel projection is used with the slope 7: 0.25: 2.25 and defined points every 7” along an extended chine equation to X= 294.  Although the actual chine ends at X= 213.5, the extended portion will determine the shape of the tumblehome at the stern when projected forward.  As more curvature is included in this extended curve, the tumblehome will also increase.

The entire shape is not yet designed, but sequence and type of calculations needed should be understandable.  The results, when finished, are full-size measurements in three dimensions with fair curves and excellent accuracy using simple tools.  Enough offsets are generated that all you have to do is connect the conveniently-spaced dots.

Do you find information about Boat Building Plans And Kits are you looking for? If not, below may help you find more information about the Boat Building Plans And Kits. Thank you for visiting, have a great day.

Read More..

Wooden Boat Plans Australia | A Voyage to Remember

Wooden Boat Plans Australia

                                                       A Voyage to Remember, Miami to Panama

When we were snorkeling in Maui recently, talk turned to snorkeling in Panama and our life there.  I recalled an exciting trip I took bringing a boat to Panama from Florida.  Our friends suggested that the trip was interesting and unique enough that I should record it on paper.  So my attempt follows.

When I was on active duty in the US Navy, 1966-68, I initially attended navigation school in San Diego.  The subject was interesting enough to me that I graduated #1 in my class, and continued to study available nautical references on board the two ships on which I served.  Spending many hours per day on the ship’s bridge deck for months at a time (crossing the Pacific twice, navigating the Mekong Delta, patrolling the Vietnam coast and Gulf of Tonkin, and cruising to Japan for maintenance) provided plenty of time for such review.  I became an enlisted supervisor in the navigation department.  Later, in 1976 while visiting Hawaii, I picked up a reference on Polynesian navigation techniques (We, the Navigators) to help understand how the early voyagers were able to find their way in the ocean’s vastness.  In late 1980, our family was living in Panama.  My assistant and her husband were buying a used 46’ trawler (single diesel engine) in Florida which they intended to bring to Panama to live and cruise on.  They asked me if I would act as navigator for the trip from Miami to Colon, Panama.

They offered to pay for my flight to Miami, which I declined.  If I were to do this, I wanted it to be from a sense of friendship rather than any monetary obligation.  I provided a list of the different nautical charts, references, and instruments which would be necessary for such a trip.  My assistant’s husband, Charles, was a retired US Navy diver who now worked for the Panama Canal Company.  He was to fly to Miami and spend one week examining and preparing the boat, including obtaining the necessary navigation supplies, before we left port.  He was one very tough individual and totally fearless.  He recruited a third crew member, Bill, who I hadn’t previously met but who seemed like a solid character.  It would be just the three of us on a quick voyage back to Panama.

I had talked to one of my patients, then employed as a canal pilot, who had previously been a Caribbean charter captain.  He gave me a route recommendation, which appeared reasonable, and loaned me his sextant.  I flew to Miami on a Saturday in early December, took a cab to the yacht basin, and was prepared to leave harbor the following morning.  Upon arrival, I asked about the navigational charts and references and was stunned to discover that none of the publications I requested had been purchased because it was now December 6 and the contained data was only good through the end of the year.  They were deemed too expensive to obtain for such a short period of use, but, without the sight reduction tables, the sextant was useless.  Also, only one chart had been obtained.  It was an overall chart showing Miami toward the top edge and Panama at the bottom edge.  With such a large area to cover, the chart lacked any detail of depths and features of the various coastlines.  Additionally, the trawler had only been maneuvered on various headings once to check the accuracy and deviation of the compass.  The boat was equipped with a radar set, but the range was only a few miles.  LORAN coverage of the southern Caribbean was lacking at that time, and GPS had not yet been invented.  This was shaping up to be quite a challenge, and I was glad I had some knowledge of navigation without dependency on instruments.

Checking on supplies, the trawler was almost empty with very little on board for ballast, just some groceries, a few tools, and our suitcases.  Our only refrigeration was a single large ice chest.  On Sunday morning, we set out on our adventure.  The first leg was to follow the coast of Florida southwest to Key West, then head straight south to the coast of Cuba.  The hurricane season officially ends November 30; we were now in December but encountering strong winds.  As we headed south from Key West we were headed into night, crossing the Gulf Stream with a strong current from the west opposing strong wind from the southeast which made for large, steep waves against our under-ballasted hull.  Forty-six feet may sound like a large vessel, but, on the open ocean, it is a tiny presence.  The strong wind created a surface haze of spray allowing very limited visibility.  Instead of an enclosed bunk, I had a bed to (try to) sleep in at night.  I tried to hold onto the bed, wrapping my arms and legs around the mattress while resting, but was completely thrown out of the bed once by the lurching hull.  Once I heard a scream from Bill, “We are going over!” as the boat slid sideways down the face of a wave with the rudder seemingly useless.  Fortunately, before we were rolled in a trough by the next wave, the rudder finally caught hold and the bow came around sufficiently to face it.  When it was my time to go on watch, I filled a paper cup with water and held it in my hand.  If I were to fall asleep, I would drop the cup, and it would be my alarm.  It worked.  Everyone needed what rest they could get; there was no asking someone else to take part of your watch.

We were glad to see the morning, but were now presented with a new problem.  Our large chart showed no detail of the Cuban coast.  As we continued south, we wanted to approach the coast as a navigational reference but not get so close that Cuban gunboats would escort us into port.  The solution was Polynesian navigation using cloud formations.  Distinctive cloud formations are found over islands.  Although we never actually saw Cuba, we followed its cloud formations west along the coast while staying offshore.

As evening set in, we were ready to jump off from the west end of Cuba toward Mexico.  It is an easy dead reckoning exercise (hard to miss Mexico) but it also meant re-crossing the Gulf Stream as it flows north.  We subtracted a few degrees from our compass course to allow for the current and set off into the night.  The next morning we sighted Isla Mujeres and pulled into port for refueling.  That afternoon we headed back out to sea with Cozumel to starboard and the Swan islands as our next intended waypoint.  Heading southeast, we encountered rising wind and waves from the northeast.  As the hull angled into the face of each oncoming wave, it was obvious that the "thump, thump, thump" sound of the big single diesel slowed significantly.  The engine was losing power.  Upon inspection it was discovered that sludge, from the diesel fuel we just received, was clogging the fuel filter.  The engine was being starved for fuel.  To clean the fuel filter we needed to stop the engine.  Then it was discovered that the alternator, used to charge the batteries, was not working.  The batteries were very low on electrical charge.  If we stopped the engine, it was doubtful that the batteries held enough juice to restart it.  It was time to change course and our plan.

We turned to run with the wind toward the southwest for a smoother ride and slowed boat speed slightly to match the speed of the waves and reduce engine load.  We shut off almost all electrical equipment to save the batteries, and Charles went down in the belly of the boat, holding electrical wires by hand on the batteries until the battery acid started to bubble, in an attempt to recharge the batteries.  Through the night we steered manually, using a flashlight to read the compass, and no running lights.  When it was my turn to lie in bed, I wondered what the future would hold if that engine stopped; what bit of shoreline or reef would the drifting hull crunch coral on?  Fortunately, the engine kept "thumping".

The next morning we could see some of the Bay Islands near the coast of Honduras in the distance off to port.  The wind and waves were still strong.  Charles thought that the downwind island was Roatan and suggested we aim for it.  I pointed out that if he was wrong, we would be unable to work our way back to any of the islands further upwind.  So we angled our course to port and headed for the nearest island.  It turned out to be Roatan.  The old wooden wharf was on the lee side of the island, allowing us to get out of the wind and motor quietly up to the dock (where I was to receive quite a surprise).  I was standing on the bow, dock line in hand, peering intently at the dock’s shabby state with substantial holes punched in its gray, wooden-planked surface.  I wanted to make sure that when I leaped to the dock to tie up, I didn’t put a foot through one of those holes.  Suddenly, a young black man came out on the dock, and his first words, in clear English were, “Hey, Did you hear that John Lennon was shot and killed?”  Here I thought I was in some remote place far from the beaten path, and I was getting the latest news in my own language!  Mainland Honduras inhabitants speak Spanish, but on the Islands they speak English due to previous British influence.  In Roatan we were able to get an alternator from a wrecked yacht which Charles and Bill then installed.  The fuel filter was also cleaned, and we had a good meal and rest at anchor before leaving the next morning.

We cruised east along the Honduran coast taking turns on watch.  The following morning when I came up on deck, I was immediately concerned.  I looked down at the ocean and saw churned brown water.  I yelled to Charles that we were in too shallow of water and were in danger of running aground.  He replied that the radar range he had taken indicated that we were a sufficient distance from the beach.  I pointed out that the radar was not being reflected from the gently sloping sand beach, but from a line of tall palm trees several hundred yards behind the beach.  We immediately turned out to sea until we were in clear blue water.  Later that day we passed Cabo Gracias a Dios which held a lesson for us.  The Cabo is the outlet of a major river marking the border between Honduras and Nicaragua.  A submerged tongue of silt, an invisible delta, stretches miles out to sea at this location.  You can be miles from the coast and still run aground in very shallow water.  Several ship wrecks stood as evidence.

From here we headed south and slightly east out on the open seas, away from the Nicaraguan coast, with the next intended waypoint being the island of San Andres.  The weather was now good, and we were able to troll and catch fish for din

Do you find information about Wooden Boat Plans Australia are you looking for? If not, below may help you find more information about the Wooden Boat Plans Australia. Thank you for visiting, have a great day.

Read More..