It just happens to be that 8" per mile squared is a good approximation using small distances.
It's a good approximation for ANY distance.
1 mile | 0.00013 miles = 0.67 feet |
2 miles | 0.00051 miles = 2.67 feet |
5 miles | 0.00316 miles = 16.67 feet |
10 miles | 0.01263 miles = 66.69 feet |
20 miles | 0.05052 miles = 266.75 feet |
50 miles | 0.31575 miles = 1667.17 feet |
100 miles | 1.26296 miles = 6668.41 feet |
200 miles | 5.05102 miles = 26669.37 feet |
500 miles | 31.5336 miles = 166497.53 feet |
1000 miles | 125.632 miles = 663337.65 feet |