>If the real purposes of the chariot and the accounts of it were amusement and impressing visiting foreigners, rather than actual long-distance navigation, then its inaccuracy might not have been important.
If the south-pointing chariot were built perfectly accurately, using a differential gear, and if it travelled on an Earth that was perfectly smooth, it would have interesting properties. It would be a mechanical compass that transports a direction, given by the pointer, along the path it travels. Mathematically the device performs parallel transport along the path it travels.
The chariot can be used to detect straight lines or geodesics. A path on a surface the chariot travels along is a geodesic if and only if the pointer does not rotate with respect to the base of the chariot.
Because of the curvature of the Earth's surface (due to it being curved around as a globe), the chariot would generally not continue to point due south as it moves. For example, if the chariot moves along a geodesic (as approximated by any great circle) the pointer should instead stay at a fixed angle to the path. Also, if two chariots travel by different routes between the same starting and finishing points, their pointers, which were aimed in the same direction at the start, usually do not point in the same direction at the finish. Likewise, if a chariot goes around a closed loop, starting and finishing at the same point on the Earth's surface, its pointer generally does not aim in the same direction at the finish as it did at the start. The difference is the holonomy of the path, and is proportional to the enclosed area. If the journeys are short compared with the radius of the Earth, these discrepancies are small and may have no practical importance. Nevertheless, they show that this type of chariot, based on differential gears, would be an imperfect compass even if constructed exactly and used in ideal conditions.
Ex: if a group of maybe 100 people were pushing wagons around, you only need one navigator to occasionally set south (through the use of stars, landmarks, or other navigational aids). Once south is known, everyone can "reset" the other wagons to point in the same direction.
Alternatively, it'd still be a useful aid for star-navigators who don't know any landmarks. Because you can only see the stars at night. So you could set south when the sun set. Then you sleep. When you wakeup, the wagon is still pointing south (and will continue pointing south for a few miles: until the cumulative error adds up).
A differential gear would automate all of this, but would be unmaintainable, expensive, would barely work for more than a few hundred yards, and all this in an era where labor is slave-cheap.
Another way would be to use multiple carts, only move one at a time, and calibrate it from the others, survey style. Cumulative error should be far smaller this way, and you would have fewer terrain problems.
edit: no seriously, zoom in on this pic here https://upload.wikimedia.org/wikipedia/commons/d/d6/South-po...
Huh? What kind of wheels don't turn? That's literally the definition of a wheel.
I’m on my fifth and have to confess that I’ve learned quite a bit.
The point being that it's very easy to get attached to your really cool hack but it's often best to just let it go once a better solution comes along.
But the Chariot does work as a sort of pastiche of people or organizations who don't listen or look around them.
I imagine magnetic compasses are a later invention, because they really make no sense if you can use a compass.