I'm making some calculations between lat/lon coordinates in a neighborhood. I'm running this analysis as if the Earth were flat because the planet's curvature doesn't change my calculations over the mile(ish) that I'm measuring.
How large of a distance can be accurately measured before you need to take the planet's shape into account?
For the sake of the question, let's say "accurately" means "off by less than 1%."
A quick test by R assuming a spherical, globe.
theta <- c(1:20)
a <- 6378137
l_straight <- a * sin(theta / 180 * pi) # straight tunnel
l_circ <- 2 * pi * a * theta / 360 # around the Earth
(t <- data.frame(theta, l_straight, l_circ, l_circ - l_straight, l_circ / l_straight))
And its output is:
theta l_straight l_circ l_circ-l_straight l_circ/l_straight
1 1 111313.8 111319.5 5.651557 1.000051
2 2 222593.8 222639.0 45.210387 1.000203
3 3 333805.9 333958.5 152.573436 1.000457
4 4 444916.3 445278.0 361.616996 1.000813
5 5 555891.3 556597.5 706.186385 1.001270
6 6 666696.9 667916.9 1220.085639 1.001830
7 7 777299.4 779236.4 1937.067215 1.002492
8 8 887665.1 890555.9 2890.821708 1.003257
9 9 997760.4 1001875.4 4114.967591 1.004124
10 10 1107551.9 1113194.9 5643.040973 1.005095
11 11 1217005.9 1224514.4 7508.485382 1.006170
12 12 1326089.2 1335833.9 9744.641582 1.007348
13 13 1434768.6 1447153.4 12384.737413 1.008632
14 14 1543011.0 1558472.9 15461.877671 1.010021
15 15 1650783.3 1669792.4 19009.034026 1.011515
16 16 1758052.8 1781111.9 23059.034974 1.013116
17 17 1864786.8 1892431.3 27644.555840 1.014825
18 18 1970952.7 2003750.8 32798.108827 1.016641
19 19 2076518.3 2115070.3 38552.033107 1.018566
20 20 2181451.3 2226389.8 44938.484975 1.020600
So the threshold distance would be somewhere around 1,500 kms (or 950 miles).
You may want to use geosphere package for more accurate calculation.
