Switchback Theory and Principles:

Definition of 'switchback' (and exegesis). ¹

It is necessary to carefully define what a switchback is, as over the years absurd definitions and meaningless distinctions have led to a profound misapprehension of the concept – and consequently to a lot of seriously bad trail.

As an example, there is a whole class of definitions that painfully attempt to distinguish "switchbacks" from "climbing turns". And then, not having a good handle on the essential elements of a switchback, frequently proceed to define "climbing turns" along the lines of "wide radius turns" which "do not exceed the maximum permitted grade". This suggests that switchbacks do exceed the permitted grade. Which in fact many do, but that is a consequence of bad design, not a defining element. Other putatively authoritative sources (see examples ) describe switchbacks as zig-zags (correct, but woefully inadequate), "a road or trail joined by hairpin bends" (putrid), characterized by "sharp", "sharp 180-degree turn", or even "dramatic sharp" changes in direction, making a "flat turn", and travelling diagonally. Switchbacks are said to be difficult to construct (certainly true if one does not understand the principles), and generally to be avoided. The U.S. Forest Service definition:

A reverse in direction of a trail grade with a level landing used to change elevation on a steep slope, usually involving special treatment of the approaches, barriers, and drainages.

is hardly better, as one can reverse the direction of a grade with drain dip, and change elevation with steps – and this bit about special treatment is hardly a defining element of a switchback.

These diverse, trivial, and even contradictory views show that there has been no concurrence as to what a switchback is. The laborious effort to distinguish switchbacks from "climbing turns" is invariably relative, a matter of degree only, distinguishable only if one picks contrasting instances and ignores all of the middle instances that smoothly transform one instance into the other. In all of these cases I believe the authors tried to extract a definition from various generalizations, and although some of them came close to the core of the matter, none really got to the essential part. Therefore we need to consider the meaning and derivation of the term.

The invention of the switchback and derivation of the term is credited to the Mauch Chunk Switchback Railway in Pennsylvania (USA), circa 1843. This was a gravity railroad where cars descended a series inclines connected by switchbacks. (See diagram, right.) From "A" a car rolls downhill, gathering momentum that takes it through a switch at "B". A slight ascent at "C" stops it, then sends it back to the switch, which has automatically closed, sending the car down the next incline to "D". Here it passes through another switch, comes to a stop at "E", and repeats the process. Although the core sense of the term is the wye ("Y") configuration where travel is forward and then backward through a switch, railway engineers subsequently applied the term more generally to any configuration where a grade doubled-back on itself (the characteristic "zig-zag") to gain (or lose) elevation, even when the wye was replaced with a turn, and travel proceeded continuously, without backing. ² This is in accordance with modern trail usage, where the zig-zags known as "switchbacks" are invariably traversed as turns, without any backward motion. From these and other considerations a reasonable, consistent, and – most importantly – useful definition of a switchback can be derived, as follows.

The essential definition of a switchback – not to be confused with any non-essential glosses or tips – is this:

          Reversal of a traverse by means of a wye or turn.

Where a traverse is the crossing of a slope from one side to the other, and traverses reverse when their direction across the slope (left to right, or right to left) changes. A single switchback makes a "zig" (V-shape); stacking of multiple switchbacks results in the familiar "zig-zag" pattern. But not all zig-zags of a trail (road, queue at the airline counter, etc.) constitute a switchback: there must be a reversal of a traverse.³

(As to why a traverse reverses: it runs out of slope. More particularly, the available width of the slope is not sufficient to accommodate the run (length) needed to attain the elevation required at the grade permitted. Or there has been enough run that the elevation desired can be reached on the return traverse.)

A wye is where two sets of tracks (typically rail, but can also be road) merge into one; the shape is as the letter "Y". (See the "Multi-path Landing" diagram; the green path traces a wye.) In railway usage – where the term "switchback" comes from – there would be a switch to direct movement from the stem (or tail) to one branch or the other.⁴ The notable point is: there is no turn. A train arrives from one branch, the switch is thrown, and the train then backs up (or down) the other branch. The motion or progress is still towards the destination, but proceeding foremost is the former back end of the train, which seems to have magically reversed itself end-to-end (see diagram). Note also that which ever side of the train was facing the slope will remain facing the slope.

On the other hand, when a traverse reverses by a turn – such as with trail, and most roads – the front end stays foremost, but the side next to the slope alternates with each traverse. (See the "Multi-path Landing" diagram; the red path traces a turn.) Also, motion can be continuous; there is no need to stop and reverse.

There are some wonderful examples of switchbacks on the old Great Northern mainline at Stevens Pass. Take a few moments to study them.

Not all turns reverse a traverse. Consider the "Two Turns (1)" diagram below. Which of these two turns is a switchback? Is it:
   a) the upper-right turn?
   b) the lower-left turn?
   c) both?
   d) neither? or
   e) can't tell due to insufficient data?

The turn in the upper-right does feature the "sharp short radius" and other features that accord with our prejudices of a "switchback", and even seems to connect two reversed traverses. Whereas the lower-left turn is such a "wide" turn that many trail builders undoubtably would deem it a "climbing turn". In fact the correct answer here is: insufficient data.

Take a look at "Two Turns (2)" below, which shows the same trail but with contour lines added.

It turns out that some key information was missing. E.g., the upper-right turn is wrapped around a ridge (or is it a ravine? does it really matter?); it pretty nearly follows the contours, ascending (or descending) at a fairly steady rate from end to end. Alternately, the slope it is crossing is consistently down (let us say) on the right. This is not a switchback, just a traverse following some abrupt changes in topography. ⁵

On the other hand, following this trail up from the bottom of the diagram shows one long, wide-radius turn with slope (the blue arrows indicate the fall-lines) going down on the left-hand side of the trail until the red arrow, where the trail is pointed (headed) straight up the slope. As the trail continues to turn the slope is now down on the right-hand side. This traverse has reversed its direction across the slope. The radius of the turn is wide and the angle is broad, but it is a switchback.

(Did someone say climbing turn? Consider that most distinctions between these and switchbacks – see the examples – are relative, of degree only. They can be smoothly transformed into the other with no particular demarcation; there is no innate difference, only an artificial distinction that only confuses and conceals the real essentials of turns. More on this later.)

Crossing the fall-line is a key characteristic of any turn that connects a pair of reversed traverses. The fall-line (not to be confused with a notable line of water falls on the Atlantic seaboard) is the direction straight down (and up) the slope, perpendicular to the contour line at any given point. It is, at any given point, the direction water (or loose debris) would flow (or fall) down the slope. To cross the fall-line refers not to the track of the trail across any particular fall-line, but where the heading (the direction one is headed) crosses from one side of the fall-line to the other. This is what distinguishes the turn of a switchback from any other curve or bend in a trail: a switchback turn crosses the fall line, thereby reversing the traverse. Merely changing the direction of the trail, "sharply" or not, is incidental. The angle of the turn, the length and radius, matter not; crossing the fall-line is both necessary and sufficient to reverse a traverse. Alternately, it is a consequence of the reversal.

Another consequence of crossing the fall-line is that (lacking any special construction or excavation) at the point where the tread is pointed straight up or down the fall-line the grade of the tread will be the same as the slope. It does not matter if the radius is "wide" (as some people would distinguish "climbing turns") or not; when the turn (any turn) crosses the fall-line it will be as steep as the slope. (Unless special measures are taken, such as excavation.)

Can traverses be connected by landings? Of course. More generally, and topography permitting, landings can be inserted anywhere on any traverse. But that is only a physical variation that does not change the topology. In transiting from a traverse to a reversed traverse the pattern traced on the landing will be (effectively) either a wye or a turn. With a large enough platform wayfarers could do either. Or a schottische, or even run a three-dimensional maze (e.g., see the blue path in the "Multi-path Landing" diagram ⁶). But topologically the net result will be either a wye or a turn. If the wayfarer comes out reversed from the way he went in, the pattern he traced is effectively a wye. Else it is a turn. And we need not see the details to ascertain the result. We could even throw a tent over the landing, and still determine whether the internal topology is a turn or a wye simply by comparison of the input state against the output state.

Are landings (relatively level or otherwise) required for switchbacks? ⁷ No. A "level landing" is required only for a wye, or, as will be shown later, in the special case of a zero-radius turn. Such a requirement implies a zero-radius turn (or possibly a wye), but I have yet to see any definition mention a zero-radius turn.

For some real world examples take a look at the bit of map below (courtesy of Dale Sanderson) of the Georgetown Loop:

Georgetown Loop. Copyright 2002 by Dale Sanderson

All this is in a narrow valley that descends to the northeast (right side). The yellow line is the former route of highway U.S. 6; it clearly switchbacks up the north slope. The two turns in the railroad grade west of "Hall Tunnel" are also switchbacks.⁸ (Not necessarily in the limited sense of a wye and and a switch, but in the definition here of a reverse of a traverse.) But what should we call this loop in between?

Follow the railroad grade as it ascends from the right. It is on the south slope, with the slope rising on the left-hand side. Then it crosses this relatively level area as it turns to the north. But now it is on the north slope, with slope still rising on the left-hand side. Then it loops around the historical marker and crosses a bridge back to the south slope, with the slope again rising on the left-hand side. For all that this grade has made two 180° turns in order to "gain elevation", it is not a switchback, but an elaborate traverse that makes adroit use of the topography. Strictly speaking, this is a spiral, the significant point here being that it is not a switchback despite making two 180° turns.

It is very important to note that the results above are entirely topological. That is, actual physical dimensions and magnitudes are of no importance whatsover. This is important because the criteria by which "switchbacks" are supposedly distinguished from "climbing turns" are generally relative: "sharp" turn, "wide" turn, "relatively" level, "difficult" to construct, etc. The problem is that the values they can take are continuous, with no point where there is a definite demarcation between two sets.⁹ In other words, all of the differences by which people try to distinguish "switchbacks" (really the turn of the switchback) from "climbing turns" actually blend together without any discernible demarcation, and one form morphs into the other. There is no real difference. The apparent difference is due only to selection of contrasting instances and then ignoring all of the intervening instances that form a smooth and continuous connection between them.

I am surprised at how many people miss this, so let's run this by again: the alleged differences between "climbing turns" and "switchbacks" (so-called) are only a matter of degree on aribitrarily chosen parameters. Select any pair of instances, and they are connected by a continuous range of values. There is no difference except one of degree, no special point where, all of a sudden, there is some difference that would require a distinctly different treatment. No real difference, and no basis for the distinctions trail-builders have labored to make for so many years.

Turns may indeed climb, but use of "climbing turn" as some sort of foil to "switchback" is useless, and has been the cause of profound confusion and incredible waste. Such usage should be abjured, rejected, and abandoned!

Right: U.S. Route 40 near Berthoud Pass (Colorado, USA). Photo by Gregg Gargan (CDOT).

Are these switchbacks? Or climbing turns?

The essential aspect of a switchback is the reversal of a traverse (or joining of a pair of reversed traverses) that produces the characteristic zig-zag shape. How that reversal or join is done is a detail of implementation that does not alter the essential aspect. It would be absurd – nay, it is absurd – to insist that one zig-zag traverse is a switchback but another is not because of some arbitrary distinction that is quite imperceptible on a map, or from a thousand feet away, or even at close range lacking measuring devices. The switchback is the entire zig-zag configuration, and should not be confused with, nor conditioned upon some detail of, the turn. (See more pictures of switchbacks.)

Even though some switchback turns are constructed like wyes, they are invariably used as turns (hikers very rarely ever backing up or down a grade, and I think bikers effectively never), so the primary focus here will be on the elucidation and construction of the turn of the switchback. Later I will introduce some parameters that describe all possible simple turns, and you will see that turns are .. just turns. There is a lot more ground to cover, but if you still feel that it is important, or even merely useful, to distinguish between two classes of turns then you really should go back and study this material with more attention. Also check the footnotes for additional explanations.

Once again, the proper definition of a switchback is:

          Reversal of a traverse by means of a wye or turn. ¹⁰

It is truly as simple as that.

Back to Switchback Theory and Principles.

Notes.

1. I wish this could be briefer, but the matter has become so confused and with such strong and deep feelings that a thorough discussion is needed.
2. The classic railway engineering text that discusses switchbacks and describes various notable examples is Arthur Wellington's The economic theory of the location of railways (1904). Accessible at Google Books. The incline diagram is taken from Wellington's Figure 311 (p. 945).
3. If "reversal" is applied not to a change of direction across the slope (to the right or left) but to a change in the vertical direction of the grade (ascending or descending) – what is called roller-coastering – then there is also a zig-zag pattern, in both map and elevation views, but at right-angles to what Americans associate with switchbacks. Curiously, what Britons associate with "switchbacks" is a zig-zag in this sense of a rollercoaster. (See Wikipedia: Switchback Railway.) It seems that both senses were applicable to the original instance (at Mauch Chunk). I know of a switchback turn that nearly accomodates both senses in rising slightly before doubling-back and descending. As this tends to irritate users ("why am I ascending only to immediately descend?") and invites shortcutting, it is considered to be poor design. Therefore the definition here is limited to reversals of direction across the slope, not reversals of grade.
4. On railways wyes are often arranged with another track to form a triangle (three-point turn), and used to turn around rolling stock. The use of such configurations affects only the orientation of the rolling stock, not the direction of the line or the grade, and so are not considered switchbacks.
5. Similarly with the loop of Hwy. 2 east of Scenic (the blue loop in the lower right-hand corner of Diagram 2): the highway is following the contours (not shown) in and out of a canyon; the topography changes but the direction of the traverse relative to the topography never reverses.)
6. There many possibilities. E.g., I was tempted to replace the loop of the blue path on the upper left with two wyes; the result would be exactly the same because two wyes are equivalent to a turn (see note 2). In the end there are only two possibilities (short of getting swept away by an avalanche, or some such): one exits front-end first, or reversed.
7. Switchbacks are sometimes characterized as using a landing or platform for the turn. The U.S. Forest Service defines a switchback "with a level platform", and in various editions of the Trail Construction and Maintenance Notebook distinguishes "switchbacks" from "climbing turns" on the basis of having (or not) "a relatively level constructed landing". However, it will be shown later that a level landing is required only in the special case of a zero-radius turn. In all other cases a turn – what many people think of as "the switchback" – can be constructed without a landing.
8. Sharp-eyed readers may notice that the first turn – the portion above "ek" – follows the contour around the turn (with the slope up on the right). The slope was up on the left before that, so (you might wonder) where did the traverse reverse?
      Over the creek. This is tricky because at the point of reversal the grade has not yet started turning. The trick is that the contours turned. Only they don't do it right there, they run up the creek a bit to do the deed, then come back innocently parallel but going the opposite direction. Topologically it is no different than if the grade had gone out on a trestle and made the turn "in the sky", then returned to the slope. The question is whether it then turns left, or right; that is, whether the slope ends up on the same side, or opposite side. Here it turns left; in the parallel case at the western end of the loop (where it also crosses the creek) the grade turns right. This is an odd case, but fortunately not one that need overly trouble us.
9. I believe many people accept these supposed distinctions because in their mind they see examples which are clearly distinguishable into two sets. However, that is only because their sample set is incomplete, and does not include any examples with intermediate values. As an interesting exercise, consider any criterion by which one may be distinguishing these two kinds of turns, and some value that criterion might take. Then expand (or contract) it. For sure, things can get mighty ugly, but is there any point where suddenly one type of turn turns into the other? Are we not really looking at turns, whose characteristics vary as different parameters vary? We will look at this in greater detail later.
10. I shan't say this is the only possibility; I will be curious to see if any improvements can be made. But after several years of analyzing this and related matters I think this definition beats out any other I have yet seen.