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Practical
Nautical Formulas:
Displacement-Length Ratios:
Sept/Oct 2003 Ocean Navigator Magazine - Unltralight Displacement
between 50-100, Light Displacement is 100-150, Moderate Displacement
150-220, Heavy Displacement 220-300, More than 300 is very heavy.
D/L Ration - use long tons, 1 ton = 2,240 lbs, divided by the cube of the
waterline length divided by 100:
(Displacement/2,240)
(LWL/100)3
Hull
speed (knots) = 1.34 x square
root of waterline length (in feet)
Distance
to Horizon (nm) = 1.17 x square
root of height of eye (in feet above sea level) deck
at about 5' above water on Creative Touch, assume 5' eye (10’ total height of
eye), then 3.7 nm to horizon
Range a
light can be seen in distance (combination of two
distances to horizon)
= (1.17 x square root of hgt of eye) + (1.17 x
square root of hgt of light)
compare
this distance with nominal luminescence range of light
Distance (nm) to
object by vetical sextant angle, corrected for
dip, when base of object is visible:
=
hgt of object (feet)
6076 x tangent (vertical angle)
Distance to
object (nm) when bottom of object is beyond
horizon:
= square root of :
( tan (vertical angle)
)2 +
h
-
tan (vertical angle)
.0002419
.7349
.0002419
h = difference between hgt of object and
hgt of eye. Vert. angle corrected for index error and dip.
Draft
of vessel when heeled = draft x cosine
(heel angle)
Speed (kn) of
wind-driven current = 0.03 x (wind speed in kn)
Maximum
Wavelength = 1.5 x square root of fetch in nm
Wave speed in
knots = 1.34 x square root of wavelength in feet
(or)
Wave speed =
3.03 x (wave period in seconds)
Velocity made
good = boat speed x cos (angle off true wind)
Tide rises or
falls these fractions of its range during
these hours:
1/12
-
first hour
3/12
-
4th hour
2/12
-
2nd hour
2/12
-
5th hour
3/12
-
3rd hour
1/12
-
6th hour
Tide
will have risen or fallen these fractions of its
range after these successive
hours:
1/12
- after 1st hour
9/12 (3/4) - after
4th hour
3/12 (1/4) -
after 2nd hour
11/12
-
after 5th hour
6/12 (1/2) -
after 3rd hour
12/12
-
after 6th hour
Change in height
of Tide: =
h/2 x (1-cos(180o x time ratio))
h
is total change in tide hgt between high and low. The time ratio is time elapsed
from the previous tide divided by the time difference between the two tides.
(Similar to rule of 12 above)
Flow
rate of leak in boat:
Q = 3,600 (A) (H)
Q = gallons per minute of water coming in
A = area of hole in square feet
H = height of water over hole in feet, to bottom of
the opening
Patch
or cover thickness to withstand water pressure (patch over hole):
T = square root of:
48 (H) (L2)
1000
T = thickness of wood or plywood patch in inches
H = height of water above bottom of hole, in feet
L = length of patch, longest distance between
supports, in feet
GROUNDING
FORMULAS:
How hard aground, in weight:
TPI = (L)
(B)
600
TPI = Tons per inch of waterline immersion
(amount of weight needed to raise or immerse the boat's hull 1 inch)
L = waterline length in feet
B = waterline beam in feet
Force needed to pull the boat
off aground: F = (R)
(U)
F = force needed in lbs
R= lbs aground (from TPI formula)
U= friction; mud=.3, sand=.4, coral=.7, rock=1.5
Breaking
strength of sythetic line (nylon/dacron) = C2
(2,400)
BS = breaking strength in pounds
C = circumference in inches
conservative estimate for dry clean rope.
safe load
about 1/3 of Breaking Strength
Pulling strength: 100 shaft
horsepower equals one ton long pull (2,240 lbs)
under ideal conditions. (50% of this in reality)
Flotation:
(7.44 gallons per cubic foot)
Sea Water
=
64 lbs / cubic foot
or =
8.6 lbs / gallon
Fresh Water =
8.3 lbs / gallon
Diesel Fuel =
7.0 lbs / gallon
Liters/Gallons:
3.78 Liters/Gallon, 0.264 Gallons/Liter
Gallons/Cu
Ft:
7.44 gallons / cubic foot
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