What the map is doing
An astrocartography map is a birth chart redrawn across the surface of the Earth. The birth moment is fixed and the viewing location varies. Wherever Saturn would have stood exactly on the eastern horizon, the western horizon, the meridian overhead or the meridian below, a line is drawn.
The method is modern. Jim Lewis worked it out in the 1970s, and it is a technique of the computer age rather than an inheritance from antiquity. What it takes from older astrology is angularity, the long standing rule that a planet on one of the chart's four angles counts for more.
Meridian lines and horizon lines
The Saturn MC and IC lines mark the longitudes where Saturn was culminating and where it was at the lowest point respectively. Because both positions sit on the meridian, and the meridian is a fixed great circle through the poles, these lines draw as straight verticals on the map at every latitude.
The AC line, where Saturn was rising, and the DC line, where it was setting, follow the horizon instead. The horizon's angle to the ecliptic changes as latitude changes, so the point that is rising drifts, and the lines curve. Toward the poles they can bend severely. It is worth stating this because the standard illustration shows four lines that look alike, and a reader who believes that will misread every high latitude map they see.
What Saturn's lines are read for
Saturn signifies time, limit, structure, obligation, endurance and the consequences of things. On the MC line the tradition reads career built slowly, authority earned rather than granted, and responsibility that arrives whether or not it is wanted. The named difficulty is a long stretch of little visible reward, and public scrutiny that does not let much slide.
The IC line is read as a heavy or serious private life, obligations to family, and a sense of being weighed down at home. It is also read as somewhere a person builds a base that lasts.
The AC line is described as being met as reserved, older than one's years, self-controlled, with isolation as the standard caution. The DC line reads through others, associated with committed and long lasting partnerships and with relationships that impose duties.
All of this is interpretation. It says what has been read into the symbolism, not what a place will do. A Saturn line is not misfortune, and calling it that would be a claim the technique cannot support.
How far a line reaches, and how far the claim goes
The conventional orb is a few hundred kilometres, commonly given as seven hundred to eight hundred, with the reading strongest on the line and diminishing outward. That figure is repeated rather than established. No measurement produced it, and practitioners who use tighter orbs are not doing anything less rigorous.
The technique is geometry applied to a symbolic system. The geometry is exact and computable, which is exactly why the lines can be drawn to the kilometre and why every program agrees. What a Saturn line means where it crosses a given city is convention, contributed by readers over the last fifty years or so. That is a reasonable thing to think with. It is not a reason to move somewhere, or to rule a place out.
Two related ideas fill in the picture: parans, latitudes where two planets are angular together, and the relocated chart, which redistributes the houses for a chosen city and often says more than the lines alone.
Questions people ask about this
Is a Saturn line something to avoid?
The tradition reads Saturn lines as demanding rather than as misfortune, with structure, duty and slow progress as the themes. Nothing on a map justifies ruling out a city.
What is the Saturn MC line read as?
A place where career is built slowly and responsibility arrives. The appeal is authority that lasts, and the difficulty is a long period of visible effort with little visible return.
Why do Saturn AC lines bend on the map?
Because rising lines follow the horizon, whose tilt against the ecliptic depends on latitude. The bend is a real feature of the geometry and becomes dramatic near the poles.
What orb is used for Saturn lines?
The same as for any other planet, about seven hundred to eight hundred kilometres, strongest on the line. That range is a convention of the literature rather than a measured effect.
When was this technique developed?
In the 1970s, by Jim Lewis. It is a modern technique. The principle that angular planets are emphasised is old, but drawing the result across a world map is not.
Does relocating change my Saturn placement?
Not its sign or degree, which are fixed by the birth moment. Relocating changes which house it falls in, because the houses depend on the horizon and meridian of the place you use.