Rocks, and more rocks

Rock Pile
Test rendering of a rock pile in Terragen. The height and size of the pile were calculated based on the volume of rock that would have been excavated from the cut.

A few details need to be nailed down before we can set up the Deep Cut scene. Some, such as the width of the cut, should be recorded somewhere in the historical record. Other details, like the size of the rock piles, can be calculated.

I’m still looking for a source on the dimensions of the cut. In the meantime we can start on the rock piles.

How tall were they? Contemporary sources describe them as “huge,” achieving heights of up to 50 feet.

Perhaps, but let’s see what a little math tells us.

When it comes to excavating stone, there are two important numbers: angle of repose and swell factor.

Angle of repose is the slope at which a pile of stone (or any material) remains stable. At a greater angle, gravity will overcome friction and the material will slide down the slope. For dolomite and broken rock, the angle of repose varies between 35 to 40 degrees. For now I will use the minimum angle of 35 degrees.

This makes it simple to calculate the size of a cone of broken stone 50 feet high. A 35-degree angle of repose yields a base diameter of about 143 feet.

As the tiny human figure standing next to the cone shows, this is a very large pile of rocks. Much too large based on the size of the canal cut shown in the adjacent profile. In fact, a cone this size would contain more than five times the amount of rubble that would be excavated from the cut. The crane needed to build this pile would also have to be a huge – at least 55 feet tall with a jib of about 90 feet.

Let’s approach the problem properly by starting with the volume of rock to be excavated. For this we need the second important number: swell factor.

Swell factor is the increase in volume that occurs when you break up solid material into smaller, irregular pieces. For dolomite, the factors that I’ve found vary between 50 and 67 percent, with a median of 66. We’ll use the median, which means that every 100 cubic feet of solid dolomite excavated yields 166 cubic feet of broken stone that must be piled up somewhere.

We don’t know the width of the cut yet, so for now I’ll assume a base width of 28 feet plus a 6-foot recess in one wall for the towpath. The maximum depth – which we do know – was 31.5 feet.

The cranes were placed between 60 and 70 feet apart along both sides of the canal. This means, on average, each crane handled a 32.5-foot-long section (the average distance of 65 feet divided by 2). Taking the swell factor into account, this means 50,766 cubic feet of broken stone would be lifted out of the cut by each crane.

This results in a more reasonable-looking pile. The cone would be about 29 feet high and 82 feet in diameter. This represents the maximum pile size at the deepest part of the cut. Elsewhere, the piles would be relatively smaller.

Of course, the rubble pile would not be a cone. The crane would distribute the rubble in an arc described by the tip of the jib. This would reduce the height and width somewhat, depending on the size of the arc and the length of the jib.

Rubble pile base
Plugging the results of our calculations into a set of Terragen functions produces the basic shape of a rubble pile distributed over a 50-degree arc. It’s about 23 feet high.

The math gets a little dicier now, but an equation can be plugged into Excel to test different volumes and slopes. Then functions can be used to generate the basic shape in Terragen.

Modeling a rock
How to model a rock: Basic box in Maya; subdivided, sculpted, and surfaced in Mudbox; shaded and rendered in Terragen.

After adding a few random displacements, the shape is covered with thousands of rocks. The result is shown at the top of this post. Many variations can be made and placed in the scene.

It may not be 50 feet tall, but it’s still an impressive pile of rocks.

Excavating the Deep Cut

Process of Excavation
“Process of Excavation, Lockport,” by George Catlin. Published in Cadwallader Colden’s 1825 “Memoir.” (New York Public Library)

The Deep Cut was the last section to be finished on the original Erie Canal. For nearly five years canal planners and engineers had watched with increasing frustration as an army of immigrant laborers gradually chipped and blasted its way through the solid rock of the Mountain Ridge.

Now known as the Niagara Escarpment, the ridge is composed largely of Lockport dolomite and extends across western New York. It forms the ledge that Niagara Falls tumbles over 20 miles to the west. And in the 1820s it stood squarely in the canal’s path.

There was no alternative: The canal had to go straight through the ridge to reach Tonawanda Creek to the south, and then on to Buffalo and Lake Erie. To maintain a water level equal to Erie meant digging more than thirty feet deep in places. Through solid rock. With hand tools and primitive blasting powder.

“Through that ridge,” wrote the state’s canal commissioners in their annual report for 1822, “occurs the most extensive deep cutting, which we have any where to encounter. It is, in truth, very formidable, and exceeds seven miles in length.”

Niagara Escarpment
The Niagara Escarpment can be clearly seen in this oblique aerial view facing southwest over western New York. Made with digital elevation data from the U.S. Geological Survey, the image reveals the surface stripped of all foliage and color. The dotted line traces the path of the canal. The vertical scale has not been exaggerated – to canal engineers in the 1820s, the escarpment truly was a formidable barrier.

The excavation of the Deep Cut will make an excellent subject for a digital scene. To a large extent it will be inspired by George Catlin’s well-known lithograph, Process of Excavation, Lockport, which may be the only contemporary depiction of the effort.

Catlin, who would later become famous for his portraits of Native Americans, was commissioned to execute a series of scenes to commemorate the canal’s completion. His sketches were among the first lithographs printed in the United States when they appeared in Cadwallader Colden’s Memoir in 1825.

As art, Process of Excavation is undeniably dramatic. Lowering clouds and towering piles of rubble frame a deep vertical cut in which masses of men break and haul stone. Explosions roar in the distance. Overhead, spindly horse-powered cranes haul out the rubble to raise in piles fifty feet above the canal’s banks, according to the accompanying text in the Memoir.

The image has a certain Dante-esque feeling to it, of men laboring ceaselessly in the first circle of Hell.

As a historical reference, however, the lithograph raises a few questions. The rock piles seem too steep and too high, the canal cut too wide. There is little detail in the cranes. In fact, there is remarkably little detail anywhere. The indistinct mass of laborers in the bottom of the cut blends right into the rock walls.

Our goal will be to build a scene that is historically accurate and physically realistic. And despite the questions that remain, there’s no harm in starting on some of the details.