3 ms·

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

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.

dragontamer 7y ago
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. ------ 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).
jasomill 7y ago
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.

dragontamer 7y ago

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. ------ 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).

jasomill 7y ago

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.