National standards for horizontal and vertical accuracy of topographic maps were

Question

National standards for horizontal and vertical accuracy of topographic maps were adopted in 1941. The standard for horizontal accuracy requires that no more than 10 percent of the well-defined map points tested shall be more than 1/50 of an inch out of correct position at scales of 1:20,000 or smaller.

A) For maps of scale 1:24,000, 1/50 of an inch on the map corresponds to how many feet on the ground?

B) For maps of scale 1:62,500, 1/50 of an inch on the map corresponds to how many feet on the ground?

C) For maps of scale 1:250,000, 1/50 of an inch on the map corresponds to how many feet on the ground?

D) For maps of scale 1:2,000,000, 1/50 of an inch on the map corresponds to how many feet on the ground?

Explanation / Answer

A) Map scale is = 1 : 24,000, that is, 1inch in map scale is equal to the 24,000 inch in the ground.

12 inch = 1ft.

So, 24,000 inch = 2,000 ft

According to map scale 1 inch is equal to the 2,000 ft in the groud

So, 1/50 inch = 2,000 / 50 = 40 ft in the ground.

B) Map scale is = 1 : 62,500, that is, 1inch in map scale is equal to the 62,500 inch in the ground.

12 inch = 1ft.

So, 62,500 inch = 5208.3 ft

According to map scale 1 inch is equal to the 5208.3 ft in the groud

So, 1/50 inch = 5208.3/ 50 = 104.166 ft in the ground.

C) Map scale is = 1 : 250,000, that is, 1inch in map scale is equal to the 250,000 inch in the ground.

12 inch = 1ft.

So, 250,000 inch = 20833.33ft

According to map scale 1 inch is equal to the 20833.33ft in the groud

So, 1/50 inch = 20833.33 / 50 = 416.66 ft in the ground.

D) Map scale is = 1 : 2,000,000, that is, 1inch in map scale is equal to the 2,000,000 inch in the ground.

12 inch = 1ft.

So, 2,000,000 inch = 166666.66 ft

According to map scale 1 inch is equal to the 166666.66 ft in the groud

So, 1/50 inch = 166666.66 / 50 = 3333.33 ft in the ground.

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