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288Re: [AtkinBoats] Displacement for America Junior and Silver Heels

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  • jkohnen@boat-links.com
    Aug 14 7:25 PM
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      On Thu, 5 Aug 2004 05:31:44 -0600 (MDT), Chris K wrote:
      > Anyone know the overall displacement for America Junior and Silver Heels?
      > ...

      It's unfortunate that the Atkins didn't supply displacement information with
      most of their published plans. But there are ways to guestimate the
      displacement of a boat from limited information. One way is to take the
      study plan and figure the aproximate area of the midship (largest)section,
      either by pretending that it's made up of rhomboids and triangles, or by
      laying a piece of transparent graph paper over the section and counting the
      squares (find out the area of each square at the scale of the plan). Then
      multiply the resulting area by the waterline length and multiply that by the
      "prismatic coefficient" to arrive at a good guess of the hull's underwater
      volume. One cubic foot of salt water weighs about 64 pounds, so multiplying
      the volume by 64 will give you the displacement.

      I've stolen the following explanation from Dave Gerr's book The Nature of
      Boats (Int'l Marine, `992):

      "... Since a boat's displacement is just the volume of her hull below the
      waterline, it's a simple matter to multiply the 31.4 square feet (2.92 m2)
      of Dread Naught's midship section area times her waterline length of 44 feet
      (13.4 m) to get a volume of 1,380 cubic feet. This alone does not give the
      volume of Dread Naught's hull; however, it does give the volume of an
      imaginary object -- a prism -- the same shape as Dread Naught's midship
      section and exactly 44 feet long. (In fact, 1,380 cubic feet -- at 64 pounds
      per cubic foot, for salt water -- works out to an incredibly high 88,320
      pounds of displacement.)

      "Fortunately, there's a very simple relationship between the volume of this
      imaginary prism and the true displacement of Dread Naught, or any other
      vessel. (Sam will, no doubt, mutter some- thing about the prismatic
      coefficient.) It just so happens that almost every displacement-speed hull
      requires a prismatic coefficient between 0.51 and 0.56 for best efficiency.
      (Fifty-four percent is the usual optimum.) Dread Naught -- this case -- will
      have 54 percent of the displacement of the imaginary prism. Seagoin' Sam
      will simply multiply 88,320 pounds times 54 percent to get Dread Naught's
      displacement of 47,770 pounds. This is a good figure for a 44-foot-waterline
      craft, giving her a displacement-to-length ratio of 250.

      "Now, the prismatic coefficient is actually indicating how fine, pinched, or
      tapered the ends -- bow and stern -- are. A perfectly square scow or barge
      would have no taper or fineness and so her prismatic coefficient would be
      1....

      "To find the prismatic coefficient of any boat:

      Prismatic (Disp (lb) / 64)
      Coefficient (PC) = ----------------
      Midship Area (sq ft) x WL (ft)

      (Disp (kg) - 1025)
      ------------------
      Midship Area (m2) x WL (m)

      "Over the last 75 years or so, designers have learned that the faster a boat
      is intended to go, the higher her prismatic coefficient ought to be, as
      follows:

      SPEED-LENGTH PRISMATIC
      RATIO COEFFICIENT
      Displacement-Speed Boats 1.5 or less 0.51 to 0.56
      Semi-Displacement Boats 1.5 to 2.5 0.60 to 0.70
      Average Planing Boats 2.5 to 4.0 0.70 to 0.72
      High-Speed Planing Boats 4.0 and higher 0.72 to 0.78

      ...

      "... If you've ever wondered what the displacement of a particular design
      is, all you need is her waterline length, waterline beam, and depth of hull.
      Say you've fallen for a salty hooker -- Varnished Viking├╣38 feet on the
      waterline, but don't know her displacement. The info sheet says her
      beam's 12 feet 3 inches and her draft is 3 feet 11 inches. Of course, no
      one's told you this design's waterline beam; however, it's usually about 95
      to 98 percent of the overall beam. Accordingly, you can estimate Varnished
      Viking's waterline beam at 12 feet.

      "All that's left is to make a good estimate of Viking's midship area. You
      guessed it, there's another coefficient to help us out here. It's called the
      midship coefficient.... The midship coefficient is just the area of the
      midship section divided by the area of a rectangle of the same width and
      depth. An excellent average is 0.65, or 65 percent. Picture the sectional
      shape of the boat. A perfectly triangular midship section would have a
      midship coefficient of exactly 0.5 or 50 percent, whereas a perfectly
      rectangular midship section would have a coefficient of exactly 1.0 -- the
      same area as a rectangle -- because it is a rectangle!

      "This is just about what you'd find in many barges or scows. The famous
      racing E-scows have midship coefficients approaching 1.0. Shallow vee-bottom
      power craft with flatfish floors (low deadrise) and flattish-bottom sailboat
      hulls will usually have midship coefficients of around 0.73, while very
      sharp deep-vee hulls can have midship coefficients of 0.55 or so. Since
      Varnished Viking has an average midship section we'll use a midships
      coefficient of 0.65 and can figure her midship area to be 30.4 square feet
      12 ft. WL beam x 3.9 ft. depth of hull x 0.65 = 30.4 sq. ft.

      "Varnished Viking is a displacement-speed craft, so we know her prismatic
      coefficient must be very close to 0.54. A bit of multiplication gives her
      approximate displacement at 39,920 pounds -- 30.4 sq. ft. midship area x 38
      ft. WL x 0.54 = 623.8 cu. ft., and 623.8 cu. ft .x 64 lb./cu. ft. = 39,923
      lb."

      --
      John <jkohnen@...>
      http://www.boat-links.com/
      All the troubles of man come from his not knowing how to sit still.
      <Blaise Pascal>
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