3cl Jarabelo, James Paolo.
Betelgeuse
Problem Solving.
Time= distance/speed
= 6970 Nm/ 21 knots
= 331.9047/24
= 13 days .829365 x 24
= 19.905 hrs
= 54.3 min
situated time: 13 days 19 hrs. 54.3 min
21 March 2020 1820H
13 days. 1954H
4 April 2020. 1414
2D. +8
ZT = 5 April 2020 0814H
Great Circle Sailing
1. cos dist = (coslat1 x cos lat 2 x cos DLO) + (sin lat 1 x sin lat 2)
= cos 36 deg 55 ‘ x cos 51 deg 40 X cos 50 deg) + (sin 36 deg 55' x sin 51 deg 40’
Dist = cos ^-1 (0.7899098661)
Dist = 2269.37 mi
2. cos Initial course = (sin lat 2 - ( cos dist x sin lat 1)) / (sin dist x cos lat 1)
Cosco = sinL2 - (cosDxsinL1)/sin D x cos L1
Cos.Co=main 51°40’ - cos 37° 49’ 22.48 x sin 36° 55’/ sin (37°49’22.48’’ x cos 36°55
IC = N 50.79 deg W / 309.21 deg T
3. cos Final Course = (sin lat 1 - (cos dist x sin lat 2)) / (sin dist x cos
lat 2)
=SIN36° 55' - (COS 37° 49’ 22.48’’ x SIN 51° 40')/(SIN 37° 49’ 22.48’’ x COS
51° 40')
FC = -0.04986254384
FC = cos A-1 -0.04986254384
FC = W 2.86 deg S
FC = 267.14 deg T
4. cos lat V cos lat 1x sin 50.79
Lat V = = COS L36° 55’ x SIN 50° 47’ 14.34’’
Lat V = 0.6194876412
Lat V = cos ^-1 0.6194876412
Lat V = 51 deg 43' 16.58”
5. sin Dlo V = Cos I.C / sin Lat V
DLO V = cos 50° 47’ 14.34’’/sin 51° 43’ 22.8’’
Dlo V = sin^-1 0.8052987206
Dlo V = 53 degrees 38 20.81"+ 140 deg W
Long V = 193 deg 38' 20.81"
6. Tan lat X1 = cos DLo V - X1 x Tan Lat V T
Lat X1 = Tan^-1 Cos 10 x tan 51 deg 43 ° 16.58"
Lat X1 = 51 deg 17’38.32"
Longx1 = 41deg 17.7’
7. Tan lat X2 = cos DLo V - X2 x Tan Lat V
Lat X2 = Tan^1 cos DLo V - X2 x Tan Lat V
Lat X2 = 49 degrees 58'35.78"
Long x2 = 31 deg 17.7’
8. Tan lat X3 = cos DLo V - X3 x Tan Lat V
Lat X3 = Tan^-1 cos DLo V - X3 x Tan Lat V
Lat X3 = 47 degrees 39'33.22"
Longx3 = 21 deg 17.7’
9. Tan lat X4 = cos DLo V - X4 Tan Lat V
Lat X4 = Tan^-1 cos DLo V - X4 x Tan Lat V
Lat X4 = 44 degrees 8'55.78"
Long x4= 11 deg 17.7
10. Tan lat X5 = cos DLo V - X5 x Tan Lat V
Lat X5 = Tan^-1 cos DLo V - X5 x Tan Lat V
Lat X5 = 39 degrees 9'50.09"
Long x5= 1 deg 17.7’
Composite Sailing
L 35" 40 N
L2 37 49'N
LV 45" 00 N
long | 141"0 0'E
Long2 122" 40'W
Dlo = 96 20 E
a). To find the Longitude where the track meet;
COS PI = TANLI/TANLV
= TAN 35" 40' / TAN 45"
= 0.7177
PI = 44 deg 08.1' E
Long 1= 141 deg 00.0' E
Long V1 = 174 deg 51.9 W
b). COS p2 = Tan L2 / Tan Lv
P2 = Cos^-1 0.77568 P2=39deg 08.0’W Long2 = 122 deg 40' W
Long V2 = 161 deg 48.0 W
c). To find the Initial Course:
SIN A = COS LV / COS L1 =COS45 COS 35* 40
IC = N 60.5 deg E
D.) Sin FC = cos Lv/COS L2
= COS 45 deg/ COS 37 deg 48'
FC = S 63.49" E
COS AV1 = SIN L1 / SIN LV
= SIN 35 40 / SIN 45"
= 34.45" x60'
AVI = 2,067.2miles
COS BV2 = SIN L2 / SIN LV
= SIN 37deg 48/ SIN 45"
= 29.91 x 60’
BV2 = 1794.8nm
P3 = Dlo - (P1+P2)
= 96 deg 20’ - ( 44 deg 08.1’ + 39 deg 08’)
P3 = 13 deg 03.91’
V1V2 = P3 x 60 x cos Lv
= 13 deg 03.9’ x 60 x cos 45 deg
V1V2 = 554.3 miles
Total composite distance = 2067.2 + 1794.79 + 554.3
Total composite distance = 44q6.29 miles
