Place a square grid on a round planet
A survey team is working on a flat level area. They start their measurements from a position on the 50TH parallel i.e. their latitude is 50 deg North. They measure 24 miles due North, then 24 miles due West, then 24 miles due South, and finally 24 mile due East.
What is the position of the end point with respect to the starting point?
Assume the earth’s radius is 3959 miles.
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1 solution
Let Q =Starting lat = 50 deg is 50 x 360 \2 xPi rad = 0.87266 rad
Let R =Displacement north of 24 miles on earth’s circumference. =24/3959 rad = .006021 rad
S = Q +R = lat of north . = .878727 rad
Distance east/west around globe at lat Q is COS (Q) 3959 X 2 X pi. = 15989.4 miles
Distance east/west around globe at lat S is COS (S) 3959 X 2 X pi. = 15873.6 miles
Difference in circumferences around = 115.8 miles
Difference in feet = 115.8 *5280 = 611476 ft
Portion of a full circumference in 24 miles = 24/15873.6 = .0015119
Portion of change in each 24 mile= .0015119 X 611476 =924 ft