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On the Map

Deliver Me From Danger: How Steep Is My River?

By Tamia Nelson On the Map

March 24, 2015

Few movies are memorable. But the 1972 film Deliverance had staying power, and it left an enduring mark on the American consciousness. For one thing, it helped to get many of us interested in whitewater canoeing, while teaching would‑be paddlers a few important lessons in the process. And no, I'm not talking about the need to master the art of archery. The risk posed by homicidal backwoodsmen acting out American Sniper fantasies is, in reality, vanishingly small. But even if the woods are safer than the streets of many cities, there's danger to be found on the water, and that danger was trailed early in the film, in an acrimonious exchange between Lewis and one of the Griner brothers. When Lewis is asked why he wants to take a canoe down the doomed Cahulawassee River, he answers flippantly: "Because it's there." To which the Griner brother responds, "It's there, all right. If you git in there and can't get out, you're goin' to wish it wudn't."

He had a point. Lewis and his companions might as well be running a river on the far side of the moon. They even have trouble finding the put‑in. And there's no better way to get into trouble than to leap (or paddle) into the unknown. Worse yet, this was willful ignorance on the part of the four buddies who set out to canoe the Cahulawassee. They had a good map. In fact, that map is the first thing the reader encounters in James Dickey's novel:

IT UNROLLED SLOWLY, forced to show its colors, curling and snapping back whenever one of us turned loose. The whole land was very tense until we put our four steins on its corners and laid the river out to run for us through the mountains 150 miles north. Lewis' hand took a pencil and marked out a small strong X in a place where some of the green bled away and the paper changed with high ground, and began to work downstream, northeast to southwest through the printed woods.

This scene never made it into the movie. But it's clear from the book that none of the four men seated around that table in the bar — not even Lewis, supposedly an experienced canoeist — did more than give the map a cursory glance. And they pay a terrible price for their folly.

The prudent paddler shuns adventures of the sort that drive novelists' plots. She knows better than to blindly go where no woman has gone before. So whenever I plan a trip, I make a map or chart my first port of call. And despite the proliferation of interactive electronic maps — not to mention high‑resolution satellite photography of all the world's once‑secret places — I still find that nothing gives me a feel for the lie of the land like a paper quadrangle. Not even the television‑sized monitor on my desktop computer can match a quad's sweep and scope. It's not either‑or, of course. Like most paddlers, I find value in both paper and pixels. But paper remains my first choice for planning and on‑the‑water navigation. I like to know that my safety doesn't depend on the state of charge in a battery.

That being the case, let's …

Look at a Map

And the map we'll be looking at is the Tallulah Falls, Georgia, 7.5‑Minute Series (1:24,000) quadrangle. It depicts the gorge of the Tallulah River, the real‑life river that the movie‑makers chose to stand in for some of the livelier bits of Dickey's fictional Cahulawassee. I downloaded the map from the United States Geological Survey website, and I've reproduced part of it below. (Right‑click on the image to enlarge it.)

Do I Hear Banjos?

You can learn a lot about the river with just a quick glance. For example, you can see that (1) it flows generally southeast, (2) it's dammed (meaning that water levels and discharge won't necessarily reflect local rainfall and natural runoff), and (3) the gorge is a gorge in fact and not just in name. Even before you know the contour interval (20 feet), the crowded tracery tells you that the river valley has mighty steep walls. You'll find it instructive to sketch a profile, but simple arithmetic alone will tell you that the gorge is between 500 and 600 feet deep.

Which leaves one important question unanswered:

How Steep Is the River?

It's obvious at the outset that this stretch of the Tallulah isn't a millpond. The contour lines cut the river again and again in the bend below the dam. Of course, this isn't the Cahulawassee. That river existed only in Dickey's imagination. But if the map he described at the start of the book boasted a similar riparian staircase, it would certainly have lent force to the Griner brother's warning. And if Lewis had taken note of just this one thing, and no more, he and his three companions would have had fewer "adventures." That said, it's often useful to be able to put a number to the rather amorphous notion of steepness. So let's see how that's done.

Begin with the contour interval. I've already mentioned it: 20 feet. But if you're looking at another topographic map for the first time, you'll find the answer in a flash. It will be printed just below the graphic scale, and you can also get it simply by inspection. Count the lines between labeled contours and divide. But be careful: Some maps have supplementary intermediate contours on the flats. Don't be led astray by these. You'll also need to know the units. Does the contour line labeled "1800" mean 1800 feet or 1800 meters? The map's legend will tell you. Make sure you check.

We're almost there. We need only one more piece of information before we can get started: the map's scale (aka its "representative fraction"). Once we know that, we can determine distance, and with distance and drop we can calculate steepness. But there's no mystery about the scale, either. The representative fraction (1:24,000, in this instance) will be printed on the map. (NB: In creating illustrations for this article, I've enlarged the Tallulah Falls quad. Furthermore, I've no way of knowing what sort of display you're viewing this on. It could be a tiny tablet — or a monitor the size of small table. Either way, the quad's representative fraction won't tell you anything useful unless you have a copy of the paper map in front of you. But the graphic scales in the portion of the map I've reproduced below are in proper proportion.)

Scale Model

Now we have all we need to determine how steeply the river drops in its run though the gorge. The contour interval gives us the drop in feet. The scale gives us the distance in miles. And dividing drop by distance gives us average gradient. (That's engineer‑speak for steepness. Sticklers for precision will point out that gradient is a vector quantity, incorporating direction as well as magnitude. We needn't concern ourselves with such niceties, however.)

Are you ready? Then let's …

Crunch the Numbers

First, though, I'm duty‑bound to note that the figure we'll generate, useful as it is for planning purposes, can also be misleading. It's an arithmetic average, and averages conceal as much as they reveal. Many of you will have heard the joke about the homesteading pioneer who drowned while fording a river with an average depth of one foot. (He stepped into a ten‑foot‑deep hole.) And if Alice Walton ever had occasion to sit down around a big table with a hundred Walmart "associates," the average wealth of the people in the room would be truly eye‑watering. But it's not likely that any of the associates could afford a private jet. Or even one of the wheels. The bottom line? Averages are slippery things.

Nonetheless, average gradient can give you some idea of a river's runability. In my experience, any stretch of river that drops more than 10 feet to the mile will warrant thoughtful consideration, especially by paddlers in loaded canoes, and an average drop of 50 feet per mile will challenge even strong parties of experts in flotation‑filled boats. (It goes without saying that no amount of map work eliminates the need to scout any rapid before running it. At least I hope it does.)

Enough preliminaries. It's crunch time. And the drill is simple:

  1. Choose starting and ending points. If possible, begin where a contour crosses the river.

  2. Count the contours between the start and the end, assigning 0 to the contour line at the starting point (i.e., 0, 1, 2, … ).

  3. Multiply that number by the contour interval. This is the total drop.

  4. Now measure the distance (in miles or kilometers) between starting and ending points, following the river's twists and turns as best you can. This is the total distance.

  5. Divide the total drop by the total distance. The result is the average gradient in feet per mile (or meters per kilometer).

OK. Let's calculate the Tallulah's gradient from the bridge where the highway crosses the river to the point where Cascade Falls tumbles down. Not counting the contour under the bridge (Contour 0), but including the line just downstream of Cascade Falls, 14 contours cut the river in this stretch, for a total drop of 280 feet. Measuring the distance along the river gives 0.5 miles. The result? An average gradient of some 560 feet per mile.

That would be an exciting downhill on a bike, but in a boat… I think I'd opt to portage. What about you?

Just for fun, let's compare this rather alarming figure with the average gradient for the entire 1.6‑mile run from the highway bridge to the map's edge. Twenty‑four contour lines cut the river in this stretch. That means the river plummets 480 feet in those 1.6 miles, or a bit more than 300 feet to the mile. (Why "a bit more"? Because the river drops an unknown distance between the last contour and the edge of the map. The extra drop will be less than 20 feet, though, and this won't make much difference to the average.) A final observation: The river descends 200+ feet in the 1.1 miles between Cascade Falls and the map's edge, an average of "only" 180–200 feet to the mile. I'm still not tempted to run it, I admit, but I'll bet others are. And good luck to them.

There you have the story of average gradient, a handy tool for sizing up a river. It's no substitute for scouting, however: As we've already seen, averages can and do mislead, sometimes with terrible consequences. But average gradient does serve as a sort of go / no‑go gauge to a river's runability — so long as you always read "go" as "maybe," that is!

Show Me the Way

No prudent paddler runs a river without checking it out on the map first. This means more than giving the map a hurried once‑over on your way to the put‑in. You need to go to school on your map. And you can start by running the numbers on drop and distance. Once you have these, you're ready to compute average gradient. Why is this important? Knowing the gradient is the key to unlocking many of a river's secrets. It won't tell you what's safe to run, but it can give you a pretty good idea where you'll have no sane alternative but the portage trail.

In other words, you don't have to wait for someone else to deliver you from danger. You can do it yourself. That's a good feeling, isn't it?

The map used to illustrate this article was excerpted from a digitized quadrangle produced by the United States Geological Survey. And this bounty is made freely available to paddlers — not to mention hikers, climbers, and cyclists — for the price of a click. Why not use the contact link at the USGS Map Locator website to say thanks?


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