PRIMITIVE NAVIGATION PROJECT By Alper Can Yildirim Aim

PRIMITIVE NAVIGATION PROJECT By Alper Can Yildirim

Aim : To find the latitude and longitude of Cambridge by tracking the shadows of a stick during different time periods of the same day.

Equipments • • Foot long stick Cf. A’s roof A digital watch Tape Measure

a straight wooden stick. The shadow of the stick The surface

How do we calculate θ ? tan θ = length of the stick / length of the shadow So; θ = tan-1 ( Lstick / Lshadow)

Military Time (hours) Shadow Length (feet) Tanθ Θ (degrees) 9: 12 9. 2 3. 12 0. 321 17. 8 9: 30 9. 5 2. 79 0. 358 19. 7 10: 06 10. 1 2. 38 0. 420 22. 8 10: 30 10. 5 2. 29 0. 437 23. 6 11: 06 11. 1 2. 12 0. 471 25. 2 12: 06 12. 16 0. 462 24. 8 13: 06 13. 1 2. 43 0. 412 22. 4 13: 42 13. 7 2. 81 0. 356 19. 6 14: 36 14. 6 3. 98 0. 251 14. 1 15: 06 15. 1 5. 92 0. 169 9. 6 15: 18 15. 3 7. 40 0. 135 7. 7

Vertical Angle vs. Time of the Day V e r t i c a l A n g l e Time of the day (hours)

Local Area Noon (LAN) and Meridian Height (MH) M H LAN

Taking the derivative y = -1. 286 x 2 + 29. 82 x – 147. 4 y’ = 2*(-1. 286) x + 29. 82 = 0 (setting it equal to zero to find the x and y coordinates of the vertex) x = LAN = 11. 59 hours 11: 35 AM Y= MH = 25. 49°

Latitude from meridian height of sun Meridian height Latitude = 90 o+Decl-Meridian height Due South

Latitude of Cambridge Latitude experiment = 90° - 21. 87° - 25. 49° = 42. 64° Cambridge = 42. 38° Error = 0. 26° = 15. 6’ Declination value for December 2 is taken from the website http: //www. wsanford. com/~wsanford/exo/sundials/D EC_Sun. html Declination of sun @ December 2 = -21° 52’ = -21. 87°

Conversion to UTC • LAN = 11: 35 • LAN + 5 hours + Eo. T = UTC • We need to find the Eo. T for December 2. from the equation of time graph.

Longitude of Cambridge • The difference between UTC and 12: 00 will give us the longitude. • LAN + 5 hours + Eo. T = 11: 35 + 5 h + 10’= 16: 45 • 16: 45 – 12: 00 = 4 h 45’ = 4. 75 h • 1 h = 15° • Therefore 4. 75 h = 71. 25° • Cambridge = 71. 11° • ERROR = 71. 25°-71. 11° = 0. 14° = 8. 4’