PRIMITIVE NAVIGATION PROJECT By Alper Can Yildirim.

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Presentation transcript:

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 CfA’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 ( L stick / L shadow ) tan θ = length of the stick / length of the shadow So; θ = tan -1 ( L stick / L shadow )

Military TimeTime (hours) Shadow Length (feet) TanθΘ (degrees) 9: : : : : : : : : : :

Vertical Angle vs. Time of the Day Vertical AngleVertical Angle Time of the day (hours)

Local Area Noon (LAN) and Meridian Height (MH) LAN MHMH

Taking the derivative y = x x – y’ = 2*(-1.286) x = 0 (setting it equal to zero to find the x and y coordinates of the vertex) x = LAN = hours  11:35 AM Y= MH = 25.49°

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

Latitude of Cambridge Latitude experiment = 90° ° ° = 42.64° Cambridge = 42.38° Error = 0.26° = 15.6’ Declination value for December 2 is taken from the website C_Sun.html C_Sun.html Declination of December 2 = -21°52’ = °

Conversion to UTC LAN = 11:35 LAN + 5 hours + EoT = UTC We need to find the EoT 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 + EoT = 11:35 + 5h + 10’= 16:45 16:45 – 12:00 = 4h 45’ = 4.75 h 1 h = 15° Therefore 4.75h = 71.25° Cambridge = 71.11° ERROR = 71.25°-71.11° = 0.14° = 8.4’