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South-Pointing Chariot (wikipedia.org)
75 points by benbreen on Oct 25, 2019 | hide | past | favorite | 22 comments



Without a compass, it seems like this would cumulate error in less than a mile that would make it useless for navigation. A turn or two of one wheel would make the doll point in the opposite direction, yet driving over rough terrain for a mile would cumulate at least a few turns difference. It seems like this is its true purpose instead:

>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.


The fun part of this article for me is the bit relating such a chariot built with a differential gear arrangement to the differential geometry of the surface upon which it travels:

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.


Alternatively, it could have been used as a way to "mass-produce" a well known result.

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.

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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).


If I had to build something like this in 1000 BC, I'd use a cart with wheels that did not turn at all and put a heavy statue on top. Then, whenever it came time to change direction, I'd get a few guys to hoist the statue up, while someone else rotated the cart independently. (And there are easily mechanical ways to make this process simpler.) You could recalibrate using the sun or stars.

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.

EDIT:

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.


I think you're assuming their roads were straight. This wouldn't work at all on a winding road/trail where turns are constant.


It would be a massive annoyance, but would still work better than a differential gear made with the materials science of the time. I personally think that the story is fantasy.


There's nothing particularly difficult or expensive about a wooden differential.

edit: no seriously, zoom in on this pic here https://upload.wikimedia.org/wikipedia/commons/d/d6/South-po...


At some point, a massive annoyance asymptotically approaches physical impossibility.


Or to have two statues on the same cart, or to keep some sort of a more discrete and orientable object on the same cart to keep track.


> cart with wheels that did not turn at all

Huh? What kind of wheels don't turn? That's literally the definition of a wheel.


Rotate about the axle, but not turn from side to side.


You can still rotate the entire chariot. There’s a vertical axis of rotation through each wheel. Think about how you can rotate a wheelbarrow by rotating the entire thing at once. The tire doesn’t spin, but you’re still rotating.


Perhaps he meant a fixed axle, so both wheels have to turn at the exact same rate. Still doesn’t make much sense though, it would be incredibly inefficient to have to lift up the statue every time the road changes direction ever so slightly.


Harder to do that with a 4 wheeled cart.


The object we're discussing is a two-wheeled cart.


Not in the earliest record, presumably the only eyewitness account.


Here’s a terrific explanation of how differential gears work, from a film produced by GM in the 30s: https://youtu.be/yYAw79386WI


That really is a great explanation - thanks for linking it. The whole playlist deserves a watch: https://m.youtube.com/playlist?list=PLI7lqC4ZBnInJOAwogQJtSq...

I’m on my fifth and have to confess that I’ve learned quite a bit.


A number of years ago I read a book about the invention of the Segway (https://www.amazon.com/s?k=1578516730) and apparently Dean Kamen used a "south-pointing chariot" as a metaphor for a really cool hack that is subsequently made unnecessary by a superior technology.

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.


Who knows, but it's possible that this invention was originally meant kind of tongue-in-cheek. I think any mechanical designer who could understand how differential gears produce this result would also be aware that small errors (skidding of one wheel or whatever) would accumulate. Also it really invites comparison to a magnetic compass, which is much simpler, cheaper, more foolproof, and probably also invented in China.

But the Chariot does work as a sort of pastiche of people or organizations who don't listen or look around them.


It looks like a nice solution for navigating a forest or a desert during the mid hours of the day without getting lost, requiring only a calibration at morning.

I imagine magnetic compasses are a later invention, because they really make no sense if you can use a compass.


I was so fascinated by this invention as a kid that I tried to build it with Lego.




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