Download - Sailing
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CELESTIAL NAVIGATION Section 17
The SailingsThe Sailings
Prepared by: John C. HudsonSaanich Peninsula Squadron, VISD Jan 2006 / Rev. Jan 2007
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Sailings used for such things as:
- determining distance and course between 2 known points
- finding point of arrival after travelling given distance and
course
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- for short distances, information can be obtained by plotting on
Mercator Chart
- for longer distances, easier to use mathematical solution with
calculator and trigonometrical functions
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These methods are called The Sailings
- types of sailings are:
- Plane Sailing (this section)
- Mid-Latitude Sailing (this section)
- Traverse Sailing (section 18)
- Great Circle Sailing (section 19)
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The Sailing Triangle
- boat sails distance “D” from point “X” to “Y” on course angle “C”
- boat moves north a distance of “XZ”
- if Latitude of“X” and distance“XZ” known,Latitude of“Y” can becalculated
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The Sailing Triangle
- not as easy to calculate Longitude of “Y”
- distance covered by a degree of Longitudevaries withdistance fromequator(section 15.1)
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Latitude and Departure
- distance in miles “XZ” known as difference in Latitude “ ”
- distance inmiles “ZY” iscalleddeparture “p”
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Latitude and Departure
- units of measure are as noted in triangle
- if distance “D” and course angle “C” known, “ “ and“p” can becalculated usingtrigonometricalfunctions
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Course in a Quadrant: azimuth angle or direction between 2 points as measured from either a northerly or southerly meridian in an
E or W direction
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Course in a Quadrant- angle can never exceed 90º
- 4 quadrants are NE, SE, SW and NW- actual course sailed is “Cn” to indicate
measured clockwise from N
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Plane Sailing (use if sailing < 100 miles)
triangle XP1P2 formed by:
- meridian throughpoint of departure P1
- destination atparallel of Latitude P2
- course P1 to P2
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Plane Sailing
Sin C = p / DCos C = / DTan C = p / where
D = distance travelled (miles)
= difference in Latitude (miles or arc)
p = departure (miles) or difference in Longitude (arc) C = vessel’s course (in quadrant)
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Plane Sailing Example
- find difference Latitude “ “ and departure “p”, if D = 15.6 miles = D Cos C = 15.6 Cos 27º = 13.9 miles
p = D sin C = 15.6 Cos 27º = 7.1 miles
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Mid-Latitude Sailing (use if sailing < 1000 miles)
- meridians of Longitude converge towards North and South Poles
- distance covered between meridians of Longitude is dependent on Latitude
- Mid-Latitude sailings more accurate than plane sailing but less accurate than
other methods
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Mid-Latitude Sailing
- to convert departure “p” (miles) to difference in Longitude “DLo” (degrees
and minutes of arc), first necessary to calculate Mid-Latitude “Lm” (degrees)
- “Lm” is arithmetical mean of initial Latitude L1 and final Latitude L2
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Mid-Latitude Sailing
Mid-Latitude (Lm) = (L1 + L2)/2 or
= L1 +/- (1/2) *Example:
if L1 = 33º N and L2 = 35º N
Lm = (33º + 35º)/2 = 68º/2 = 34º
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Mid-Latitude Sailing
- having derived Mid-Latitude “Lm” (degrees), difference in Longitude “DLo” calculated by: (answer in minutes or miles and has to be converted to
arc degrees and minutes)
DLo = p / Cos Lm
where: - departure Latitude = L1
- destination Latitude = L2
(L1 & L2 in degrees and minutes)
- departure = p (miles)
- diff. of Latitude = (miles)L1
L2
Lm
DLo (degrees & minutes)
(miles)
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1) Mid-Latitude Sailing - find Cn and D, given point of departure L1 and Lo1,destination L2 and Lo2,
steps: Lm = (L1 + L2)/2
calc DLo & convert to minutes
p = DLo Cos Lm
= L1 ~ L2
C = Tan-1 p / then get quadrant Cn
D = / Cos C
Lm
DLo
L1,Lo1
L2,Lo2
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1) Mid-Latitude Sailing – Example:- point of departure L 43º 13.5’ N, Lo 57º 18.3’ W
- point of arrival L 15º 27.1’ N (error in text), Lo 19º 22.1’ W - find Cn & D:
Lm = (43.225 + 15.452)/2 = 29.339º N
DLo = (57º 18.3’ - 19º 22.1’) = 37º 56.2’ = 2276.2’ to E
p = DLo Cos Lm = 2276.2 Cos 29.339º = 1984.2 miles to E
= 43.225 – 15.452 = 27.773 = 1666.4 miles to S
C = Tan-1 p / = Tan-1 1984.2/1666.4 = S 50.0º E
Cn = 180º - 50.0º = 130.0º
D = / Cos C = 1666.4 / Cos 50.0º = 2592.5 miles
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2) Mid-Latitude Sailing - find destination
L2 and Lo2, given point of departure L1 and Lo1, Cn and D
steps:find C quadrant from Cn = D Cos C (miles to degrees)
L2 = L1 ± (degrees & Min.)
P = D Sin C (miles)
DLo = p / Cos Lm
Lo2 = Lo1 ± DLo
Lm
DLo
L1,Lo1
L2,Lo2
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2) Mid-Latitude Sailing – Example: point of departure L 48º 20.2’ N, Lo 7º 02.1’ W
course 253º, distance 2382 miles, find destination:
C = 253º - 180º = S 73º W = D Cos C = 2382 Cos 73º = 696.4’ or miles
= 11º 36.4’ to S
L2 = 48º 20.2’ N - 11º 36.4’ N = 36º 43.8’ N
p = D Sin C = 2382 Sin 73º = 2277.9 miles to W
Lm = (48.337º + 36.730º) / 2 = 42.533º
DLo = p / Cos Lm = 2277.9 / Cos 42.533º = 3091’ = 51º 31.3’ to W
Lo2 = (7º 02.1’ W + 51º 31.3’) = 58º 33.4’ W