Switchback Theory and Principles:

Grade.

Why grade is important.

To build sustainable trail in soil across slopes one of the most important factors, if not the single most important factor, is: grade. As this is not yet a commonplace view I shall need to explain and support it.

There are various reasons why people will build trail, but I am going to assume that everyone who has gotten this far in the theory of switchbacks wishes to avoid tread failure. It is unaesthetic, it reflects poorly on our personal and organizational competency, and it is a waste of resources.

I am also assuming that most of us are concerned with how to do a lot of trail work with limited resources. Given limited resources it is often tempting to try to get by with the minimum of effort and resource necessary. Be careful to not scant that minimum! Work that fails is not only wasted, it may also increase the work needed for repair. Given limited resources it is all the more important to be concerned about how to avoid the waste of failure.

In my early days we wanted to maximize the amount of trail we constructed. Unfortunately we seemed to have often scanted the minimum work required. At one point I estimated we were spending roughly 40% of our time in repair and reconstruction of trail – and this was not 10 or 15 year old trail that needed some rejuvenation, but often new trail only a year or two old. Nor was it a simple matter of some locations needing much more effort; in some cases the fix that endured did not seem to be much different or more extensive than the original work that had failed.

I suspected that the difference between trail work that lasted and trail work that soon needed repair had something to do with how it was routed, but I was not able to articulate that view because I did not understand the essential elements.

One of the principal modes of failure that we encountered was loss of tread due to erosion. Now back then we knew what the cause was: it's the water. And we knew what to do about such problems: fix the drainage. This even makes sense if erosion is defined (as some folks do) as the loss of tread material due to water. If "fixing the drainage" (usually involving outsloping, drain dips, water bars, or ditching) didn't fix the problem, well, go back and fix it better!

The USFS Trail Construction and Maintenance Guide of 1996 did say:

  It is much more important to understand how the forces of water and
  gravity combine to move dirt than it is to dig dirt ....

That could have provided a clue, but it came after I got started.

Early on I noticed some anomalies. Like seeing water flowing across and down a trail without causing any damage. (This may seem odd to many of you simply because you have seldom noticed it. But even if you avoid hiking in heavy rain, you have undoubtably seen, many times, the little windrows of fir needles, or other signs, that indicate water has flowed down a trail. Most likely it has been doing so many years, with little or no damage.) And I saw erosion where there was no water. Now the latter is often "obviously" due to boots (even hooves and wheels), but this contradicts the notion that tread erosion is a drainage problem, so it tends to get ignored.

Several years ago I finally made the key observation: erosion – whether by water or boot soles – correlates with grade. Or rather, to steep grades. I confirmed this one summer by closely monitoring a section of heavily used trail on a weekly basis for two months. There was no rain in this period, and the boot density (and other factors)1 can be considered constant through the section. The erosion – and there was discernible erosion in this period – at each point correlated with: the grade. At this point I realized: water is not the cause of erosion, but only its agent. The cause is steep grade.

That is important enough to bear repeating: water is not the cause of erosion, but only its agent. The cause is steep grade.

Critical grade.


      Full-bench subgrade diagram. 
      [halfdome-mw.jpg 23 KB]

Don't forget the key caveat here: we are building tread in soil. No soil? Hey, no problem! Here we see the final ascent on Half Dome (Yosemite N. P.). It's rock, no concerns about erosion, so it's straight up the slope. Trail construction here is absurdly simple: string the wire cables every spring, and pick them up in the fall. Also intensely unchallenging.

Photo by M. Warson.

With some others I also surveyed a lightly used but seriously eroded trail in a different context, measuring the grade and looking for correlations with erosion. A curious pattern emerged. Sections over 25% grade were all heavily eroded (and had to be replaced). Sections under 20% were, with one or two exceptions, hardly eroded at all. And there were no instances of grades in the 20 to 25% range.2 In other words, erosion is not something inherent in grade that simply increases with the grade, and you pick whatever level you want to live with. No. It is minimal below some point, and maximal above that. This is the concept of critical grade, the point where the tread can no longer resist the erosive agents. No matter how well we dig drainage, tread will fail if it exceeds the critical grade.

The critical grade is the grade at which tread will begin to seriously erode in the presence of erosive agents. It marks the limit as to how steep you can build tread in soil without failure. Its value depends on various factors, including:

and undoubtably other factors that I have not yet identified.

Exposure to direct sun turns out to be a much bigger factor than I had realized. This was dramatically demonstrated when a favorite trail of mine was logged. Sections that had been doing fine under a thick forest canopy quickly went downhill after the sun baked it, even at grades under 10%, while steeper sections in the unlogged area are still fine.

On the presumption that tread failure is wasteful, looks bad, and worth some effort to avoid, we want to avoid exceeding the critical grade. On the other hand, we do have slopes to ascend, often with limited scope and limited resources, and can't be all day or all around the mountain in doing it. So just how steep can we go? We need some idea of what the critical grade is, but determining that can be a challenge as there is no way to measure it or calculate it directly. Two approaches might be taken.

One approach to determining the critical grade is to survey existing trail in similar contexts, noting the grade, extent of erosion, and key characteristics of each section, and see where the data breaks. This is not as difficult or time consuming as it may seem, and an organization might find it useful to take some surveys (perhaps as training exercises) to get values representative of local conditions. Even for smaller repair projects it is useful to determine the original grade of the failed section(s) as part of the site survey, and then ensure that all repairs stay below that grade.

A second approach is to make an informed guess, based on experience and knowledge of local conditions, perhaps with a few choice measurements, and then be very conservative. Be careful with this! It is all too easy (and too likely) to make a guess that is more wishful than informed. Be sure that you have some basis for the number you come up with. It may be wrong, but if you want to make any improvements in the future you will need to understand the basis of your estimate this time. 3

Either way, make your best estimate of both the most likely value of the critical grade, and the lowest value you think is likely (i.e., the margin of error). Consider it like the edge of a precipice. How close do you really want to stand, particularly if you are blindfolded 4 and can't see it? And how sure are you that you really know where that edge is? (This can get very deep; consult any book on statistics or project estimation for more information.)

Allow for changes in conditions. If your trail goes through a forest that will eventually be logged, you should plan for that. Even in parks trees fall down, so there is much to be said for not pushing the limits. If conditions change – and that includes increased use because the trail has become very popular – the critical grade may change. If your margin (or allowance) for error is too small to accomodate those changes your grade may end up on the wrong side of the critical grade, and you may have to add steps to avoid loss of tread. If you have a tight spot where grade could be close to critical – and switchback turns are inherently tight spots – your design needs to be robust. This means including ample allowance for changing conditions, error in estimating the critical grade, and construction variation (discussed below). And: will the context and the design accomodate adding steps if in the end steps are necessary?

Finally, you need to decide on how much margin or cushion to allow for construction variation (I have noticed that finished grade seems to gain about two percentage points over the plan) or design changes (e.g., you need to ramp up faster than planned to go over a large root). Note that if you use up this cushion for a design change you won't have it for construction variation; in that case you will have to take extra care to ensure that construction comes out exact.

So you estimate the lowest value the critical grade is likely to be. Reduce this a little more to provide a margin for error, allowance for future changes in conditions, and yet more for a cushion for construction variation or design changes.5 The result becomes a candidate for the grade to which you will design. I say candidate, as a maximum grade may have been specified, or you may decide that for the purposes intended (know them!) a lower grade may be more appropriate. From all these candidates use the lowest one for the design grade. Don't forget that critical grade varies, so it is possible that you may have different maximum design grades at different locations. Don't forget how you arrived at this maximum design grade. (Documenting your data and your process is always a good idea.) If you get into a pinch a land manager (or other authority) might let you stretch some of these limits, but a land manager granting waivers from the critical grade would be like King Canute trying to command the tide.6

As to typical values that might be expected: I have seen cases where the critical grade appeared to be less than 10%, and one spectacular case that we measured at 50%. (Excellent conditions, including shade, and a thick layer of fir needles that cushioned the occasional heel. It was eroding, but very, very slowly.) Do not assume that one size fits all cases. Based on as yet limited experience I estimate that in most cases with good soil and shade the critical grade will lie between 14 and around 25%7, but less in poorer soils or drier climate, and much less where exposed directly to the sun.

Your maximum grade is likely to be less than the maximum grades that have been previously recommended, which range from 12% to 30%, or more. But note that these have all (as far as I can tell) been based on usability, not sustainability, and in some cases assume construction on rock. Our goal here is to avoid failure of trail built in soil.

Respect grade!

The most important principle in constructing traverses is this:

        Respect Grade!

This principle has four rules:

Let us consider these closer.

Of course not, lest ruination follow, right? Well, there is a temptation to cheat. The route you are considering is nearly good enough, and you have a conservative margin for error so you are probably not too close to the critical grade, so why not use some of the margin to get that route in? Besides, this grade stuff is just too demanding.

Resist that temptation! If you made allowance for a cushion you can use that. But beyond that you are being reckless. "Nearly" good enough is not good enough: if you exceed the critical grade your tread will fail. The point of "this grade stuff" is to avoid that. If as a result you find that some section of trail is too demanding, then that is a message you should heed. Perhaps it really does require more work and resources, perhaps it should not be built.

If you deliberately exceed the design maximum grade then you are disregarding your best estimates of critical grade and acceptable risk. You are effectively saying you will chance tread failure, only this chance is weighted against you. There is always a chance of failure, but why chase it? Take your best shot – and stick with it!

On many occasions I have heard people say: "we had to", "there was no other choice", or some such.8 I know of cases where there seems to be no feasible solution (or have we just not found it yet?), but (in trails at least) these are rare, and are special engineering challenges. For the most part, where I see trail that is too steep it was just not designed well enough, or not designed at all, or someone had no clue as to what they were doing, or could not be bothered to do it right. If you want to build trail right you will respect grade. If that is too much trouble, than that will be your reputation and legacy. Your choice.

Many trail-builders seem to think that grade is okay if its average is okay. No!

A particle of soil's resistance to the erosive forces set in play by excessive grade is unaffected by the effective resistance of other particles of soil nearby. If this particle's resistance is exceeded, it goes. That the average grade was okay makes no difference.

The Sag Curves. [sag.gif 2 KB]

A particular problem to watch out for is that the measurement of grade between any two points is only the average. If the actual grade varies anywhere from the straight line between the two points – if it rises or dips – then there will be a place where the grade is a something less, and another place where it will be a something more. Rises are not too bad, because in wearing down they tend to eliminate themselves. But dips are insidious. If the steeper part exceeds the critical grade it will erode, but the loose eroded material won't fill the dip up to the "average" grade line, as most of it moves down grade. The result is a sag that moves upward and headward (see diagram). If it doesn't founder against bedrock (perhaps leaving a wall to clamber over) it will undermine the next section of grade, continuing until there is a long, stable, low-gradient grade of loose material. In some cases the "average" grade might have been sustainable, if the dip had been filled and the over-steepened part eased. The diagram here is highly exaggerated, but this process happens even at smaller scales. So watch those dips, do not "average" grade, and measure grade from the bottom of the dip. And do not exceed the critical grade at any point!

Spiral steps. [spiral.gif 2 KB]

Another problem, and a prime cause of switchback turns eroding out, is failure to respect the inside of a turn. As will be explained later, grade is inversely proportional to the distance run. As the circumference of a turn is always smallest on the inside (think of the spiral stairs in a lighthouse), so will the grade be the greatest on the inside of the turn. If it is too steep – too bad, it will erode out, and undermine the rest of the turn. Always measure grade along the inside of a turn!

Some nice crib steps. [steps8228-3.jpg 34 KB ]

I have often heard the statement that a piece of excessively steep trail should be okay because it is "short". Wrong! As said above, grade is inversely proportional to the length or distance run. Which means that grade is improved by making it longer, but making it shorter only makes it worse. If you have an excess of rise (elevation difference or jump) that you cannot take up elsewhere, then you must build a step. Otherwise you will have a short but over-steep and very active zone of erosion that will creep up the trail in manner much like that illustrated in the Sag Curves diagram above.

This rule is really what follows if you violate the second rule. If at some point – no matter how short! – you cannot avoid exceeding the critical grade then you must build a step. 10

Note that steps do not reduce steepness, they only reduce loss of tread due to erosion. If your route is too steep, you really should find a better route. While a trail with a lot of steps might be deemed inferior, don't forget that even worse would be a trail that does not have steps – but should.

Note also that building steps – like building walls – has to be done right, and is a whole topic in itself.

In his classic text on railway location Wellington not only recommends a hand level, he absolutely states: "...no man ever acquires a very trustworthy faculty of guessing at a horizontal line."

If you don't measure it you are only guessing, which is sloppy. Recall the bit above about making your best estimate – that means taking careful measurements, and recording them. Then, and only then, do you have a basis for knowing what the true and actual situation is, and what can be done about it. (How to do this will be covered later in Measuring Grade.)

However, I recommend not using a clinometer. For sure, that would be a step up from just guessing (or not even trying), and for sure, many good trails have been built using clinometers. (Invariably by people with considerable experience, a good "eye", and a conservative approach to grade.) And clinometers are okay for route finding (reconnaissance), provided they are used properly, and their limitations understood and accounted for. But aside from that I have three problems in using clinometers to build trail: error, ERROR, and error.

For starters, most pocket clinometers generally have a precision of about two degrees, which means dealing with chunks of about 4%. 11 This is way too coarse for grade work. Second, to use one solo without setting targets and shooting up and down leads to some very large errors of estimation. (Wellington's classic text on railway engineering had an entire chapter on how "Ocular Illusions" cause misperception of grade. He stated: "To thoroughly guard against them comes with experience alone, and rarely with that."12) Third, and what I really don't like, is the all too pervasive human tendency to fudge the reading towards the desired result. The accuracy and reliability of the results are just not good enough.

There is another, deeper problem. Even the most accurate clinometer is still measuring grades as angles, and without doing trigonomery there is not much you can with angles except compare them. There is more to say about this, but first we need to cover the basic concept of what grade is.

Definition of grade: rise over run.

Even if one is not immediately involved in the measurement and calculation of grade it is necessary, in order to understand switchbacks, to have an intuitive grasp of what grade is.

Grade is either the idealized inclined plane to which we are trying to make the tread conform to, or the measurement of the rate by which this plane is rising (or sinking), measured from the horizontal as a percentage.

This is to be distinguished from slope (or sometimes cross-slope), which is either the topographic surface the trail is crossing, or the measurement of the angle of this surface from the horizontal in degrees.

These terms are analogous, but to avoid confusion they should be used with care. Grade is the inclination of the tread, measured in percent, and slope is the inclination of the topographic surface, measured in degrees.

More particularly, grade is the ratio of the rise (change in vertical distance) to the run (change in horizontal distance). Practice saying "rise over run, rise over run" – this is the trail builder's mantra. If that sounds familiar – yes! it is exactly the same as you learned in algebra about the slope of a graph. Except for two differences: 1) In algebra the ratio can be expressed in any convenient form, but in trail building we always express it as a percentage. 2) Algebraists always "sign" the value as plus or minus to indicate whether it is going up or down. However, we trail builders know that that value is exactly the same going up as coming back down (though hikers sometimes wonder about that) – and, we can tell the difference! So we use just the absolute, or unsigned, value.

Just for review, let's calculate the grade for a trail that rises one foot in the course of running five feet: Equation for calculating grade.  [grade20.gif 4 KB]

Simple! Well, perhaps that little bit of division might be scary for numbers not as well behaved as these. Don't worry, in the section on measurement are some nifty tips for finessing that.

"Rise over run" is more than the definition of grade, it is an important principle in how we think about grade. Consider: if the rise (the difference in elevation) between two points is fixed (and we do hope so, as elevation changing events tend to be calamitous), then grade varies in proportion to the run. There is a strong suggestion here: if the grade is too steep, make the run longer. The core task of building good grade is then simply finding a route long enough to accommodate the rise at a suitable grade.

The Sag Curves.  [sag.gif 2 B]

Something very important to note. A grade measured between two points describes a straight line between those two points, which has meaning only to the extent that it nearly approximates the actual surface. Take another look at the Sag Curves: If the actual surface dips below (or rises above) the measured grade line, there will be one or more places that are steeper than indicated, and possible serious consequences. Always measure a long grade at several intermediate points to ensure it is not sagging. And always measure from the bottom of any dips (unless you plan to fill them up to the grade line).

As was said above, clinometers only measure angles. Even if denoted as a percent of grade, the result is still only an angle, and without diving into some trigonometry13 the only thing that can be done with angles is to compare them (more than, less than, or nearly equal), and even that is incomplete information. This seriously constrains not only how we deal with grade, but even how we think about grade.

On the otherhand, conceiving of grade as "rise over run", and measuring it as such, is profoundly empowering. Once it is understood that "rise" problems are easily transformed into "run" problems, many problems (like the effects of various adjustments) can be solved in the field and with only simple arithmetic.

(Read about an actual case.)

How to measure grade.

While the application and use of this theory of switchbacks is dependent on actual measurements of real grades, and even on understanding how such measurements are made, yet the techniques of measurement are not an inherent part of the theory itself. Therefore they are discussed in a separate section on measuring grade.

Summary.

For trails built in soil the single most important factor in preventing loss of tread is grade. The old notion that erosion of tread was caused by water, that erosion was fixed by fixing the drainage, is incorrect: water is an agent of erosion, but not the cause. The cause is excessive grade. In particular, the critical grade is where the tread can no longer resist erosive forces. The critical grade varies depending on various factors, including soil type and exposure to direct sun; exceeding the critical grade invariably leads to loss of tread. This can be avoided by adhering to the principle of "Respect Grade!" This principle has four rules:

  1. Do not exceed the maximum grade!
  2. Do not exceed the maximum grade at any point!
  3. Too steep? Build a step.
  4. Measure it!

Key to understanding grade is the definition of grade as the proportion of "rise over run". In general rise is the challenge, run is the solution, and the core task of building good grade is finding a route long enough to accommodate the rise at a suitable grade.

At this point you should have a good grasp on what grade is, why it is important, and how to respect it. In particular: Do not exceed the maximum grade at any point!


Back to Switchback Theory and Principles.


Notes.

  1. Subsequently I recognized other factors which will be discussed later. Fortunately they were constant in this section.
  2. Why there were no grades in the 20% to 25% range I don't know. Possibly erosion initiates at around 18% and then proceeds so quickly to >25% that any transition zones were too small to get sampled. This accords with a more general observation that erosion on an inclined plane is not uniformly distributed but tends to make a sag, with the upper part getting steeper and the lower actually flatter. See the "Sag Curves" diagram further down.
  3. Record keeping. This is the basis for making any kind of improvements. I reckon that the biggest general improvement most of us could make in building trail is to measure it. After that would be recordkeeping – not only simply doing it, but, very importantly, working out how to do it effectively. But this will be a task for the next generation.
  4. And that is exactly what you are if you do not measure: blindfolded.
  5. Most of my contemporaries will likely complain that this is way too much trouble. But it is because the current generation of trail builders neglected to consider and document this kind of detail that the next generation will be bound to building, and rebuilding (and rebuilding!) substandard, non-sustainable trail.
  6. King Canute had no such misunderstanding, but apparently some of his courtiers needed a demonstration of the limitations of executive power.
  7. In my work – which is most frequently in glacial till – building to 16% grade (I have been assuming a critical grade between 18 to 20%) seems satisfactory. However, I have been measuring grade for only the last three years, and I expect it will be another five to eight years before I can decide whether my current work is sustainable.
  8. Did I hear something about having to make do with the budget one has? In the first place, there is a lot that could be said about defending your budget (but that gets into the kind of political stuff I don't want to deal with here). Second, lack of budget does not excuse bad trail. If you can't afford all the fancy (and expensive) items like crushed rock surfacing and solar-powered outhouses, fine, do them later. But do not stint the time and effort to locate the trail properly, because once it is cut in it is effectively there forever. Do not stint on the few tens of feet needed to make the grades good, because such false economies will only cost you more in subsequent maintenance, and even failure. No, lack of budget does not justify bad trail. Rather, it mandates taking the effort to do the job right, because you cannot afford not to.
  9. I am not entirely happy with this formulation, which reflects some unease that I don't really have the concept quite right here.
  10. Strictly speaking we do not need a step, which is only a shape, but a material other than soil. (E.g., a dirt step would be just awful.) A ramp of any sufficiently durable material would suffice for the narrow purpose of preventing erosion, but overly steep ramps are generally not acceptable because of useability and safety issues. Therefore we presume steps of suitable material.
  11. I have seen clinometers with precision as good as my $15 sighting level, but at ten times the cost. They are not worth it.
  12. Arthur Wellington, The economic theory of the location of railways (1904), p. 852, § 1167. Accessible at Google Books.
  13. "Diving into some trigonometry" means, in addition to basic trig skills, carrying either a table of trig functions, or a calculator. I have yet to see a calculator rugged enough to survive trail building conditions. At any rate it would be way too much button pushing when I have string in one hand, tape in the other, and pen in mouth while trying to figure how much a stake needs to be adjusted. One of the advantages of using rise over run is that much of the time the math needed I can do in my head.

Copyright (C) 2008 by J. Johnson.