How Twisty Are Rivers?

The River Jurua, in the Amazon Basin.

The objection has been raised (Hi Kyle!) that my attempt at river generation from a random walk is producing too many twists and that the rivers should be straightened out. I should note that the
example I posted was more twist-laden than a few other attempts I made, and it's quite possible to create a fairly straight section of river as well. Still, let's take a little time look at how to evaluate river bends in terms of their realism.

There are really two relevant parameters for classifying the meanders of rivers: sinuousity, and curvature radius. The former tells us how much curvature is present, and the latter tells us the distance scale on which that curvature exists. Most river valleys are relatively straight or gently bending, and so it is only the river itself that is subject to meandering within the valley.

Here's a plot of river sinuosity as a function of the local land gradient.

http://hydrosciences.colorado.edu/symposium/abstract_details_archive.php?abstract_id=183

Unsurprisingly, the more swiftly the river is descending, the less likely it is to meander. Values range between 1.2 and 2.4, with most rivers clustering above or below the value 1.5 in temperate zone. (The other cluster up above 2.0 consists of rivers in tropical rainforests.) The mean central angle of a river with a sinuosity of 1.5 is between 150 and 180 degrees. That's considerably snakier than a sine curve!

The mean radius of curvature is a little harder to explore, given more limited data. Here's the mean radius of curvature for the Colorado River:

This is roughly in the neighborhood of 1 km, suggesting that river curves are features on the scale of about a mile or so. This is, naturally enough, the distance scale of the river valley bed.

The natural conclusions are:

• Rivers curve quite a bit, frequently making the equivalent of near U-turns.
• The distance scale for these turns is fairly narrow, in particular, much narrower than 6 miles, making these features wash out except on a lower-scale map.

From a game-map standpoint this creates a dilemma, in that a map with granularity of 6 miles can't really represent the lower-scale sinuosity of the river within its bed. It seems important to be able to explicitly locate places where land is surrounded on three sides by a river, for the sake of building your own Conwy! I hate to reduce the presence of bends to something abstractly "hidden" in a hex that shows a straight river, which takes away from the fun of trying to place a stronghold location on the hex map by looking at features on the map itself.

There's a similar problem associated with the difficulty of locating a "rock dome" suitable for a high castle. You can just say that any castle in the mountains is on a dome, but most castles were built on isolated hills and domes that were not otherwise close to other mountainous features. Moreover, since rivers don't go in mountain hexes, this would make it impossible to have an elevated castle on a river (like Conwy).

Thoughts?

The Literal Atlas

Every time you see someone rolling eyes over fantasy names that feel a bit too literal, it's fair to point out that we already live in that world. Centuries of etymology have obscured the origin of most place-names, but this project by Kalimedia tracks down the original root meaning of every city, country, continent, ocean, and planet and puts them back on the map. It's somehow reassuring to learn that all along we've been living on the fold-out map from a young adult author's debut fantasy novel.

We must bear the Orb of Power across Moon Navel Gulf to Mt Noblebright!