# Transverse Mercator Projection - Spherical Transverse Mercator - Normal and Transverse Spherical Projections

Normal and Transverse Spherical Projections

Normal Mercator Transverse Mercator
The central meridian projects to the straight line x = 0. Other meridians project to straight lines with x constant. The central meridian projects to the straight line x = 0. Meridians 90 degrees east and west of the central meridian project to lines of constant y through the projected poles. All other meridians project to complicated curves.
The equator projects to the straight line y = 0 and parallel circles project to straight lines of constant y. The equator projects to the straight line y = 0 but all other parallels are complicated closed curves.
Projected meridians and parallels intersect at right angles. Projected meridians and parallels intersect at right angles.
The projection is unbounded in the y direction. The poles lie at infinity. The projection is unbounded in the x direction. The points on the equator at ninety degrees from the central meridian are projected to infinity.
The projection is conformal. The shapes of small elements are well preserved. The projection is conformal. The shapes of small elements are well preserved.
Distortion increases with y. The projection is not suited for world maps. Distortion is small near the equator and the projection (particularly in its ellipsoidal form) is suitable for accurate mapping of equatorial regions. Distortion increases with x. The projection is not suited for world maps. Distortion is small near the central meridian and the projection (particularly in its ellipsoidal form) is suitable for accurate mapping of narrow regions.
Greenland is almost as large as Africa; the actual area is about one thirteenth that of Africa. Greenland and Africa are both near to the central meridian; their shapes are good and the ratio of the areas is a good approximation to actual values.
The point scale factor is independent of direction. It is a function of y on the projection. (On the sphere it depends on latitude only.) The scale is true on the equator. The point scale factor is independent of direction. It is a function of x on the projection. (On the sphere it depends on both latitude and longitude.) The scale is true on the central meridian.
The projection is reasonably accurate near the equator. Scale at an angular distance of 5° (in latitude) away from the equator is less than 0.4% greater than scale at the equator, and is about 1.54% greater at an angular distance of 10°. The projection is reasonably accurate near the central meridian. Scale at an angular distance of 5° (in longitude) away from the central meridian is less than 0.4% greater than scale at the central meridian, and is about 1.54% at an angular distance of 10°.
In the secant version the scale is reduced on the equator and it is true on two lines parallel to the projected equator (and corresponding to two parallel circles on the sphere). In the secant version the scale is reduced on the central meridian and it is true on two lines parallel to the projected central meridian.
Convergence (the angle between projected meridians and grid lines with x constant) is identically zero. Grid north and true north coincide. Convergence is zero on the equator and non-zero everywhere else. It increases as the poles are approached. Grid north and true north do not coincide.
Rhumb lines (of constant compass bearing on the sphere) project to straight lines. Rhumb lines project to complex curves.