How the Chinese transported heavy stones from a quarry west of Beijing to the site of the Forbidden City in the 15th to 16th century is a question often pondered. In PNAS, Li et al. (2013) present an engineering analysis and offer an answer: sledging across wet ice.

The Forbidden City, Beijing, China

Why Ice?

From ancient Chinese literature, Li et al. learned that the Large Stone Carving (>300 tons) was transported to the Forbidden City on a wooden sledge that was hauled by men across an icy road, during the period between the winter solstice (December 22 ± 1 d) and late January when the average temperature in Beijing at the time was found to be −3.7 ± 0.5 °C. Although a detailed account of that event could not be found, Li et al. found a record of winter transport in 1557 via sledge of a somewhat smaller stone (9.6 m × 3.2 m × 1.6 m, ∼123 tons) along an icy road over a distance of 70 km in 28 d. The ice was made from water drawn from a series of nearby wells. That the road could support the load follows from the fact that the pressure beneath the runners, the width of which was about 20% of the width of the sledge, was ∼180 kPa, lower by a factor of ∼67 than the indentation pressure or hardness of warm ice when slowly loaded. Li et al. then ask three questions: Why did the Chinese use a sledge when wheeled vehicles were available? Was sledging on ice a good choice compared with other methods? What special features of lubrication were used? (Read full article)

The Special Method

So what special method did the Chinese follow? Li et al. note that under the conditions of the 1557 transport of the 123-ton stone, a thin (∼70-μm) layer of water would have been produced through frictional heating and melting, based upon modern research. The effect would have been to reduce the coefficient of kinetic friction to 0.02–0.03. This finding means that a thin layer of water beneath the runners of a sledge loaded to 123 tons would have reduced frictional drag by about an order of magnitude, to the extent that only ∼46 men would have been needed, well below the proposed upper limit of 300. The problem, however, was that a 70-μm layer would have frozen in less time than the 120 s it would have taken to advance a 9.6-m sledge one length when moving at 8 cm/s. To avoid that issue, Li et al. suggest that the special method the Chinese practiced was to increase the thickness of the lubricating layer by pouring water onto the icy road, perhaps to 10-times the thickness of the natural layer or to 700 μm (see Li et al.’s SI Materials and Methods). I made a calculation following the heat-transfer analysis described in Li et al.’s SI Materials and Methods and found that a layer of ∼300 μm would have been required to avoid freezing under the thermal gradient at the time. The thicker layer offered a “factor of safety” of around two that would have guarded against fluctuations in the thermal gradient.

Thus, from an analysis of frictional sliding and heat transfer, Li et al. conclude that in transporting heavy stones to the Forbidden City, the Chinese took full advantage of the natural properties of ice: of its hardness, its flatness, and its very low coefficient of kinetic friction when lubricated with water.

More Questions

Erland Schulson is Dartmouth's George Austin Colligan Distinguished Professor of Engineering, Chair of the Engineering Sciences Department, and Director of the Ice Research Laboratory.

Answers, of course, lead to more questions. I have three. A layer of water 700-μm thick is equivalent to 700 g/m2. Water of that amount is classed as flowing water, at least when present on a surface of asphalt with a slight grade. After pouring, could some of the water have flowed off the icy Chinese road, thereby reducing its thickness to below 300 μm and lessening the freezing time to below 120 s? Another question concerns temperature. If the thermal gradient is too great, water will freeze too quickly and no longer serve as a lubricant. Is that the reason the Chinese chose to move stones during the earlier part of winter when the temperature was not too far below the freezing point? My last question concerns start up. Had the sledges been placed upon planks during the daily 15.5-h interval when movement was proposed to have stopped, as Li et al. suggest (see Li et al.’s SI Materials and Methods), would their wet runners have formed a freeze-bond, leading to a high coefficient of static friction and to significantly greater frictional drag? The practice of modern drivers in cold regions to allow trucks and other vehicles to rest upon planks after running on ice [mentioned by Li et al. in their SI Materials and Methods] is not quite the same, for water would likely not be present in that kind of situation. Perhaps the Chinese altogether avoided the issue of static friction—the coefficient of which can be more than twice the value of the coefficient of kinetic friction—by not stopping movement once initiated.

Acknowledgments

This work was supported in part by the United States–Norway Fulbright Foundation Award of the Arctic Chair 2013–2014.