Return the scale factor for the angular distance from the central meridian in an (unscaled) transverse cylindrical projection

The scale factor is the distance distortion in the direction of the meridians. In the case of the Transverse Mercator projection (a cylindrical conformal projection) it holds in any direction.

Usage

scalefactor_tcyl(ang_dist)

Arguments

ang_dist: Numeric vector. One or more angular distances from the central meridian, in decimal degrees.

Value

Numeric vector, same length as ang_dist.

Details

The formulas applied are for the sphere, hence approximate.

The best known map projection system in this context is the Universal Transverse Mercator (UTM), which superposes a central meridian scale factor of 0.9996.

References

Iliffe J. & Lott R. (2008). Datums and Map Projections. For Remote Sensing, GIS and Surveying. 2nd edn. Whittles Publishing, Caithness, UK, 208 p.

Author

Floris Vanderhaeghe, https://github.com/florisvdh

Examples

x <- seq(0, 3, 0.1)
y <- scalefactor_tcyl(x)
data.frame(ang_dist = x, scalefactor = y)
#>    ang_dist scalefactor
#> 1       0.0    1.000000
#> 2       0.1    1.000002
#> 3       0.2    1.000006
#> 4       0.3    1.000014
#> 5       0.4    1.000024
#> 6       0.5    1.000038
#> 7       0.6    1.000055
#> 8       0.7    1.000075
#> 9       0.8    1.000097
#> 10      0.9    1.000123
#> 11      1.0    1.000152
#> 12      1.1    1.000184
#> 13      1.2    1.000219
#> 14      1.3    1.000257
#> 15      1.4    1.000299
#> 16      1.5    1.000343
#> 17      1.6    1.000390
#> 18      1.7    1.000440
#> 19      1.8    1.000494
#> 20      1.9    1.000550
#> 21      2.0    1.000610
#> 22      2.1    1.000672
#> 23      2.2    1.000738
#> 24      2.3    1.000806
#> 25      2.4    1.000878
#> 26      2.5    1.000953
#> 27      2.6    1.001030
#> 28      2.7    1.001111
#> 29      2.8    1.001195
#> 30      2.9    1.001282
#> 31      3.0    1.001372