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On the Map:

Going Round the Bend Again, or …
Taking the Measure of Some Map‑Measuring Tools

By Tamia Nelson
tamia@paddling.net It's Wheely Easy!

February 24, 2015

A couple of weeks back, I described four techniques that paddlers can use to answer that perennial question, "How far is it?" — where the "it" can be the lunch stop, the next campsite, the take‑out, or the nearest ATM. And I then employed each of these methods to take the measure of a particularly indecisive stretch of New York's Hudson River, as shown on the Newcomb, N.Y., 15 minute quadrangle. The map's scale (its "representative fraction") is 1:62,500. To put it another way, one inch on the map corresponds to one statute mile on the river. The correspondence isn't exact, but the error entailed in making this simplifying assumption is less than one and one‑half percent — say 70‑odd feet in the mile. I can live with that.

In any event, I ended my earlier article by promising a head‑to‑head trial to determine which of the four methods I'd just described yielded the most reliable measure of distance. That time has come. But first, to put things into context, let's pull an "official" figure out of the hat. In Alec Proskine's Adirondack Canoe Waters: South & West Flow — this guidebook was published in 1998; I've picked it simply because it was near to hand — the author gives the distance for the stretch of the Hudson between its junctions with the Indian and Boreas Rivers as eight miles. There's no indication how he arrived at that figure, however, and there's no guarantee that it's accurate, either. It will be interesting to compare it with my own determinations.
 

Now, without further ado, …

Let the Games Begin!

And the four contenders are (1) a piece of string, (2) a strip of paper, (3) a pair of dividers, and (4) my trusty opisometer. You can see them in this photo:

The Methods to My Madness

I won't describe the individual methods in any detail. You'll find that information in my earlier article, and if you haven't already read it, I'd suggest you do so now. By way of illustration, however, take a look at my initial attempt to employ string as a measuring tool. See how the river twists and turns? This is not an easy stretch of water to quantify.

Stringing Me Along

And here are the results of the first heat of my head‑to‑head trials, all of them rounded to the nearest tenth of a mile:

Measuring
  Method

String (braided cord)
Paper Strip
Dividers
Opisometer

Distance
  (Miles)

    9.8
    8.8
    8.0
    8.8

Because of the uncertainties inherent in all such measurements, I repeated each trial several times until I obtained consistent results. Paper and string required the most repetitions; dividers and opisometer, the least. To my considerable surprise, the distances determined with the paper strip and opisometer agreed. I was less surprised that the dividers yielded a shorter distance, however. As I noted in my earlier article, I'd expected this. The value determined with the string is the most puzzling, constituting as it does an outlier. Perhaps the explanation lies in the cord's relatively large diameter, which may result in overestimating the distance in river bends, an error that would rapidly cumulate. After all, as the photo above shows, twists and turns come thick and fast on the Upper Hudson.

The bottom line? I'd previously calibrated my opisometer, and its small wheel makes following even the most sinuous course comparatively easy. When care is taken to avoid backlash error, therefore, it yields accurate, reproducible results. For present purposes, then, I've taken distances determined with the opisometer as my gold standard. And that being the case, it appears that a careful paper‑strip determination will yield equally good results. (The opisometer is more consistent, however, and it's much easier to work with.) But I cannot recommend either dividers or cord. The first significantly underestimates river miles — did Proskine rely on dividers? — while the second overestimates them.

These conclusions seemed reasonable at first, anyway. But upon reflection, I still had nagging doubts. The Upper Hudson is a mighty twisty bit of water. Would dividers and cord make an equally bad showing on a less challenging river? I decided to find out. And that took me to the Kinderhook Creek, mapped on the 1980 7.5 minute Kinderhook, N.Y., quadrangle:

Down the Kinderhook

This time I measured river miles from a bridge crossing over the Kline Kill (it's located between the divider points at lower right in the photo) to the dam just above the N.Y. Route 203 bridge over the Kinderhook proper, in the village of Valatie not far downstream (just above the toothpick point in the upper left). It's a much less demanding test than the Upper Hudson, both on the map and in a boat. NB: The divider points visible in the photo are set so as to compass a distance of 0.2 miles.

Now here are the results of the second set of trials:

Measuring
  Method

String (braided cord)
Paper Strip
Dividers
Opisometer

Distance
  (Miles)

    2.6
    2.4
    2.4
    2.6

This time around, the methods show much closer agreement. Such variation as does exist — it's on the order of eight percent — is within the expected measurement uncertainty. My conclusion? On stretches of water with infrequent or large‑radius bends, all four methods yield comparable results.

I could have stopped here. But I was nagged by memories of the poor performance of the braided cord on the Upper Hudson. Would I have had better luck with a smaller‑diameter, less elastic cord? I decided to find out. So I repeated both sets of trials, substituting waxed dental floss for the nylon cord. Dental floss has a small diameter and relatively little elasticity. The wax coating also sticks to paper, making it much easier to work with.

Flossing a River

And the results? See for yourself:

Measuring
  Method

String (braided cord)
Paper Strip
Dividers
Opisometer
Dental Floss

Hudson
  Miles

    9.8
    8.8
    8.0
    8.8
    9.3

Kinderhook
    Miles

      2.6
      2.4
      2.4
      2.6
      2.4

 

OK. The dental floss did perform somewhat better than the braided nylon cord on the Upper Hudson. To be sure, it still yielded a distance that was some six percent higher than my opisometer reference value, but this difference is probably not significant. In any case, we now have enough data to work with, I think. It's time for …

Drawing Conclusions

And they're easily stated: If you're determined to string along, dental floss trumps braided nylon cord. That said, if your route doesn't involve too many twists and turns, and if you're both patient and painstaking, any of these four methods — five, counting dental floss separately — will give reasonable results. But if your chosen river can't make up its mind which way to flow, turning first one way and then another, you'd be well advised to take its measure with a paper strip — Yes, it's time‑consuming and fussy, but it's also cheap and eminently portable — or an opisometer. The latter is both quicker and less fiddly than the paper strip, of course, but you're not likely to find one for sale in the local HyperMart, and when you do run a serviceable specimen down, it won't be cheap. Nor is it something you'll be keen to use on the foredeck of a kayak in a choppy seaway.

What do I do? I use my opisometer for planning, but I rely on a paper strip under way. I reserve dividers for their traditional employment: "pricking out" a course on a nautical chart. And I save my nylon cord for tying down my tent. (The best use of dental floss is, I should think, self‑explanatory.) More importantly, perhaps, I treat all measures of river miles, however determined, as rough approximations at best, and view all estimations of travel time based on them as provisional, subject to countless corrections. Wind and wave can upset the most meticulous of schedules, as can the sight of trout rising to mayflies in a pool or a glimpse of a beaver busy at his work on a dam. Perhaps the best advice I can give any paddler (or any sailor, for that matter) echoes the principle that Thoreau articulated in his Journal: Have a broad margin of leisure in your days on the water. Then let the miles look after themselves.

This Way to Adventure

How far have we come? How much farther is it to camp? Can we do the trip in a week? These questions, and others like them, are often on paddlers' lips. And the answers can always be found on a map. But the map won't tell you anything till you've taken its measure. That's enough to send anyone round the bend. This week, though, we've taken a closer look at four ways of getting a map to talk, and we've put all of them to the test. Now you've got the tools you'll need to persuade any map to tell you what you want to know. It's a good feeling, isn't it?

Got a better idea? Don't keep it to yourself. Drop me a line and let me in on the secret. I'll pass the word along.

 


 

Related Articles From In the Same Boat
Plus a couple of single‑subject collections from our archives:
And an apposite Wikipedia article to round things off: "Opisometer"

 

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