Vince Lee's Uphill Battle
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A Hasty Experiment
Having arrived at this solution, I made a small model to illustrate the
idea and suggested we try a full-scale test to see if it would actually work. NOVA agreed, and using some skinny leftover poles and a roll of small diameter cord, we hastily tied up a sled and two ladders with which to try moving a "three-ton" rock promised by a local supplier. Due to a shortage of material, we ended up with about half as many sliders and sled crossbars as my design called for, but I figured it wouldn't matter with such a small load.
The rock finally arrived about 10 a.m. the final day of the shoot, weighing at least six tons and looking like a gigantic Idaho spud. Next to it, our sled and ladders seemed woefully flimsy and inadequate. The "crane" we expected for getting it off the truck and onto our sled turned out to be a two-ton swing arm hoist mounted on the truck; it proved all but useless. Instead, we rolled the boulder off the truck, shattering the truck bed's edge planks in the process, and watched our "moai" thud ominously into a shallow ditch.
Just getting the boulder out of the ditch and onto the sled was a huge project. We levered it up onto one of its "edges" and then rolled it onto our sled, simulating a moai in the prone position. The sled lay visibly crushed under the load, with one runner cracked and both pressed tightly into the mud of the ditch bottom with no sliders underneath. As the camera rolled, we began levering the grossly overloaded tangle of poles up out of the ditch and onto the first ladder, prying between the projecting crossbars on the sled and the ground.
It was horrendously inefficient. The levers "kicked out" as they approached the vertical,
so that much of our force went up instead of forward. Also, as we got onto the ladder,
the hastily done lashings beneath the sled's crossbars tended to hang up on the sliders.
Somewhat to our amazement, the sled nonetheless moved, and in about an hour we got
it nearly onto the first ladder. With time, energy, and daylight running short, however,
NOVA asked us to switch gears and try rotating the sled. That proved a bit easier,
since it let us turn off the fall line and across the slight grade we'd been fighting
all afternoon. In a few minutes, the sled rotated about 30 degrees.
On Easter Island, Vince Lee's team tries to lever a six-ton stone block on a hastily made sled.
One observer watching our struggle said, "Look at it. It's a mess!" I had to agree, but for
one thing: It worked. My 12-man crew had levered a six-ton rock
about 15 feet in an hour and a half. Each man had moved about 1,000 pounds of rock with no
help at all from pullers. If we'd done everything right, our performance would have been
much more impressive, but even as it was, our rate of progress (say 80-100 feet per day)
was about the same as the previous methods tested in the NOVA film with four to six times as many people.
Once underway, their sled moved much faster than ours, of course, but they lost
many hours re-rigging their gear between moves. Slow as our progress was, we could
nevertheless have gotten our "moai" up onto its ahu without anyone working on the platform's seaward side.
But could our method move an 80-ton moai, about the largest ever moved by the Rapanui
(see How Big Were They?). The problem
is partly simple arithmetic. If each of the 40 or so pullers hired by NOVA to pull the replica moai
exerted 100 pounds of force to move their sled, the friction coefficient (the ratio of the weight of a load versus the force needed to drag it) using sliders over rails must have been about .2 (4,000 pounds of force divided by 20,000 pounds of moai and sled weight = .2). Applying this coefficient to an 80-ton load requires 16 tons of forward force or 320 pullers at 100 pounds per person. My levermen were each moving about 1,000 pounds of load, which would cut this workforce in half (80 tons = 160,000 pounds / 1000 = 160 levermen). But how many men would it take if levers were used properly, correcting all the problems we encountered during our hurried test of the idea? There was only one way to find out.
The Sisyphus Project
On December 15th, 1998, my friend Bruce Davis and I collaborated on a full-scale trial
at his masonry contracting yard in Brighton, Colorado. We named our test the Sisyphus
Project after the King of Corinth whom, in Greek mythology, the lord of the underworld
condemned to an eternal afterlife of futilely pushing a large stone up a hill.
I had commissioned Mark Younghein, a log-cabin contractor in Longmont, Colorado, to fabricate a 10x15-foot sled and four 5x10-foot ladder sections from stout lodgepole pine logs. The sled weighed about a ton and the ladders were in four 500-pound sections for ease of carrying. The designs were otherwise similar to those shown in Figure 1, except that the sliders and sled crossbars were let several inches into the tops of the rails and runners, respectively, to achieve tight, rigid joints. This turned out to be an important detail. Any play in these joints greatly reduces the effectiveness of the levers, since part of each throw is wasted taking up the slack. Finally, we provided both long and short levers about three inches thick for people working atop the load and on the sled, respectively (see Figure 2).
Meanwhile, Davis's crew had constructed a scaled-down replica of the steepest ramp still existing on Easter Island (see Figure 4), a daunting 1:4 or 25 percent slope. His team also assembled several large blocks of white marble from which to select a load, depending on how many people turned out to help move it.
We notified potential volunteers and about 30 showed up on the day of the test.
Based on the idea that each person might move 1,000 pounds of rock, we played it
safe and selected a 13-ton block. We abandoned initial thoughts of using water as
a lubricant when the moisture either soaked into the soft pine logs or quickly
evaporated into the high, dry mountain air. Instead, we greased the sled runners
with lard from the supermarket on the theory that the Rapanui surely had lots of
fish oil and wouldn't have hesitated to use it.
Volunteers on the Sisyphus Project begin to rotate the 13-ton block atop the ramp.
The project we set for ourselves was simple: move the rock up the ramp and rotate
it at least 90 degrees with levers alone, using no more than the working surface
of the ramp for the purpose. After a nervous first effort that turned out to be
serious overkill, we cut the crew back to see how few people could move the sled
on level ground. Eight long levers handled from atop the rock was all it took.
Each person had a mechanical advantage of about seven, imparting about 700 pounds
of forward force—a total of 5,600 pounds for the group. Their combined weight
and that of the sled added about 3,500 pounds to the 13-ton block, so the
coefficient of friction must have been about .19 (5,600 / 29,500 = .1898).
Adding people as needed along the way, we moved the load up the steepest part of the ramp with 26 people. Unintentionally, we apparently arrived at the perfect balance between friction and mobility, since the sled tended to backslide ever so slightly when forward pressure was released. Two "brakemen" easily prevented this by jamming their levers whenever we stopped. Mechanically, the system worked exactly as expected, though the animal fat was critical to its success. Whether even better lubrication would have improved performance remains an open question. Easier uphill movement might have increased the danger of downhill slippage and created problems maintaining control of the sled.
Unlike Sisyphus, Vince Lee got what he wanted: A large block levered up a steep ramp with few people in a short period of time.
It is not known where the Rapanui rotated their moai, but to cover the worst-case possibility
we decided to do it atop the ramp, in the most constricted location of all. We easily accomplished
the maneuver as shown in Figure 3, except that by levering both sides ahead, the outside of the
turn more than the inside, we needed no pullers for forward movement onto the turned ladder. So
levers alone carried the day, and it took only about two hours to climb the 55-foot ramp and make
the turn at the top.
An Open Question
However feasible the scheme described here may be, we have no direct evidence that the Rapanui or anyone else in ancient times used it. Nevertheless, it is clear that the hundreds of people needed to drag the largest moai on Easter Island could not possibly have pulled them all the way up onto any of the numerous seacoast ahu there. They must have used some other, much more efficient transport method. The simple levering system proposed here is the only idea thus far proven to solve this problem, and it would have worked for the Rapanui and anyone else in antiquity faced with moving big rocks up steep hills and into small places. Did the ancient Rapanui do it this way? We may never know. But we now know a method they could have used, which is more than we knew before.
Vincent R. Lee is owner of Design Associates, Architects in Jackson Hole, Wyoming and a research associate both in Andean Studies at Berkeley and with the Museum of Man in San Diego. He has led numerous field expeditions and mapping projects in Latin America as well as various studies in pre-Columbian architectural design and construction techniques, particularly those involving megalithic masonry.
Images: (2,3,6,6) Courtesy of Vincent Lee
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