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

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• 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 Vikingù38 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@...>