Deadline for this submission: What’s a Son Supposed to Do? Sept. 1, 2020Due dateName

Celestial Navigation Challenge Nav Problem Narrative Sarasota Power Squadron

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Origin

Destination

Nav Problem: What’s a Son Supposed to Do?

INFO PROVIDED:Date: May 16, 2020

WT:WE: 0

Body: Sun LLSight: LANHt of Eye:

19 ft.

IC: 0Method: LOC

Sextant Hs: 47º 5.0'DR: L 23º 25.0' S

Lo 45º 15.0' WNautical

Almanac:NA2020

QUESTIONS: ANSWERS:GMT ZT

A. What is the time in GMT of LAN (Local Apparent Noon)? LAN : 14:57 11:57 SEE MT WORKSHEET

B. What is the Ho? (use LOC worksheet) Ho : 47º 15.9' SEE LOC WORKSHEET

C. What is the latitude of the observation? Lat : 23º 26.2' S SEE MT WORKSHEET

D. What is the EP (Estimated Position)? EP: L: 23º 26.2' S SEE PLOT SHTLo: 45º 15.0' W

Sight Lat/Lon

Celestial Navigation Challenge Solutions Summary Sarasota Power Squadron

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Law of Cosines worksheet - Form 96aTIME PROBLEM: What’s a Son Supposed to Do? ALTITUDE

Date May 16, 2020 Ht/Eye 19 ft.

WT 11:57:24 LAN S/M/P Star hemi Hs 47º 5.0'

WE SIGHT DATA: Body Sun LL 1 (+) (-)

ZT 11:57:24 DR L 23º 25.0' S IC 0

ZD 3:00:00 3 DR Lo 45º 15.0' W Dip XXXX 4.2'

UT 14:57:24 Total 0.0' 4.2'UT corr. 14:57:24 Corr -4.2'

G Day/Mo May 16, 2020 47º 0.8'

Ha 47º 0.8'

ALMANAC - LHA

SHA HP (moon) ___________

Sun LL (+) (-)

GHA

14 30º 53.9' Main 15.1'

57/24 14º 21.0' Add’l M/Pl

UL -30.00’

v corr Add'l Refract

Tot GHA 44º 74.9' Totals 15.1' 0.0'

45º 15.0' W DEC: 19º 17.3' N Ttl. Corr 15.1'

LHA -1º 59.9' d(+/-) 0.6 d corr 0.6' (+/- based on trend of Dec) Ho 47º 15.9'

LHA adj. 360º 0 DEC 19º 17.9' N Ho 47.265 (format for “a” calc)

INTERCEPT AND AZIMUTH calculation using the LAW of COSINES

LHA 360º 0 360.00000

LAT 23º 25.0' S 23.41667

DEC 19º 17.9' N -19.29833 - if Dec,Lat diff

(cos LHA x cos LAT x cos DEC) + (sin LAT x sin DEC) = sin Hc = 0.73474 Hc = 47.28500 º

(sin DEC - (sin LAT x sin Hc)) / (cos LAT x cos Hc) = cos Z = -1.00000 Z = 180º Zn = 0 º

cos LHA = 1.00000

cos LAT = 0.91764 Zn Calc:

cos DEC = 0.94381 Hc 47.29 º LAT LHA<180 LHA>180

sin LAT = 0.39741 Ho 47.265 º LHA 360º N 360-Z Zsin DEC = -0.33049 0.0' x 60 LAT S S 180+Z 180-Z

sin Hc = 0.73474 INTERCEPT a =

1.2 nm N 180º 180º

cos Hc = 0.67835 AZIMUTH Zn =

0 (T/A) A S 360º 0º

2012

M

m

0000

0600

1200

1800

G

g

G

SMP=1Star=2

NA2020NarrativeSolutionSumLOCMeridianTransPlotGHAI&CAltCorrArcToTime

Hr

M/Sec

Celestial Navigation Challenge Calc by Law of Cosines Sarasota Power Squadron

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Worksheet For Latitude by Meridian Transit

PROBLEM: What’s a Son Supposed to Do?

TIMEDate May 16, 2020 SIGHT DATA ALTITUDEWT 11:57:24 Body Sun LL Ht. of Eye 19 ft.WE DR L 23º 25.0' S Hs 47º 5.0'ZT 11:57:24 DR Lo 45º 15.0' W (+) (-)ZD 3:00:00 IC 0UT 14:57:24 Dip XXX

X4.2'

UT corr. 14:57:24 Total 0.0' 4.2'G Day/Mo May 16, 2020 Corr -4.2'

LAT S 47º 0.8'

ALMANAC — DEC DEC N Ha 47º 0.8'

DEC: 19º 17.3' N HP (moon) ___________d(+/-) - 0.6 d corr 0.6' (+) (-)

DEC 19º 17.9' N

Main 15.1'

TIME OF TRANSIT: Add’l M/Pl

(1) DR Lo W 360-Lo E

45º 15.0' W UL -30.00’

(2) GHA hr = 14 30º 53.9' Add'l Refract

15º -38.9' Totals 15.1' 0.0'GHA Dif 14º 21.1' Ttl. Corr 15.1'

(3) (from I&C) min/sec 57/24 57:24 (closest to) Ho 47º 15.9'(4) LAN (UT) 14:57:24(5) (+/-) ZD Lo: (W-) (E+)

3 - 3:00:00 (rev)

ZONE TIME of MT at LAN 11:57:24 LATTITUDE BY MERIDIAN TRANSITPOLE: (90º) 89º 60.0'

Steps: - Ho 47º 15.9' 1. Record DR Lo if W, or 360-Lo if E. = Zenith Dist 42º 44.1' 2. In NA find closest GHA value for MT at DR Lo (but less than DR Lo). +/- DEC - 19º 17.9' N

Note the whole hr and record GHA at that whole hr time. Lat by MT 23º 26.2' S

3. Subtract the GHA’s and locate that value in the I&C tables to determine min & sec. DR L 23º 25.0' S 4. Add m/s to whole hour to get exact time of MT (UT). a 0º 1.2'

5. Apply ZD to get ZT of meridian transit at LAN. adjust a 1.2' (nm)

Date: May 16, 2020Meridian

Transit Time (GMT)

from Daily Pages of

NA:

11:56:00

Longitude: 45º 15.0' WArc to Time conversion:

45º 3:00:00

15.0' 0:01:00TOTL Lo: (W+)

(E -)+ 3:01:00

LAN (UT) 14:57:00(+/-) ZD 3 Lo: (W-)

(E+)- 3:00:00 (rev)

ZT of MT at LAN

11:57:00

Date: May 16, 2020

Lat (S) = Zenith Distance - Dec (N)

Equator

Two ways to determine Lat by MT:

2. Calc of MT using the Arc to Time table:

1. Calc using the USPS Meridian Transit form:

NA2020NarrativeSolutionSumLOCMeridianTransPlotGHAI&CAltCorrArcToTime

Celestial Navigation Challenge Meridian Transit wrksht Sarasota Power Squadron

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R

R

Form CLS 98

Squadron

Name

1998 USPS

Sight No.

Constant Latitude Scale Small Area Plotting Sheet

UNITED STATES POWER SQUADRONS

c

50

250

240

LatMid

LatMid

LA

TIT

UD

EM

IDD

LE

LA

TIT

UD

EM

IDD

LE

350

340

330

320

310

300

290

280

270

260

230

220

210

200190 180 170

160

150

140

130

120

110

100

9080

70

60

50

40

30

20

100

50

40

30

20

10

0

40

30

20

10

0

55’

50’

45’

40’

35’

55’45º 50’ 45’ 40’ 35’ 30’

EP

1157

05’

10’

15’

20’

25’

30’

30’ 25’ 20’ 15’ 10’ 05’

1157Sun LL

44º30’45º 30’

22º 30’

23º 0’

23º 30’

30Using the USPS Small Area Plotting Sheet

Latitude SouthLongitude West

Plot using Law of Cosines

Steps:

1. Plot the current DR position

2. Plot azimuth Zn from DR

3. Plot intercept “” and LOP

4. Label appropriately

5. What is the EP?

Info from LOC worksheet:

DR position: L 23º 25.0' SLo 45º 15.0' W

Azimuth (Zn): 0ºIntercept (a) 1.2 nm A

EP: L 23º 26.2' S

Lo 45º 15.0' W

EP: L 23º 26.2' S

Lo 45º 15.0' W

S

S

W W

LOC Plot

Note: Red dotted lines used for measurement

only.

Celestial Navigation Challenge Plotting Sheet CLS 98 Sarasota Power Squadron

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