Switchback Theory and Principles:

Measuring Grade (and flagging and staking it).

Respect Grade! That is the central principle here, based on the concept of critical grade, and the assumption that we wish to avoid tread failure. Let's review it:

The fundamental basis for respecting grade is simple: measure it! Here we will study how.1

Grade is the proportion of two values, rise and run, these being the difference in the vertical and horizontal distances between two points. The measurement of grade is the measurement of these two values. As was said before, the concept of "rise over run" is not only how we define grade, it is also an important principle in how we think about grade. Grade problems typically involve two points whose vertical difference – the rise between the them – is invariant. (At least we hope so.) It is a different story horizontally. There is always a minimum horizontal difference between two topographic points (the shortest distance between them), but because the horizontal plane has two dimensions (N-S, E-W, or any equivalent) there can be an infinity of possible longer routes.2 Given a fixed value for rise, the core task of building good grade is simply finding a suitable route with a long enough run to accommodate the rise at a suitable grade. To put it very succinctly: rise is the challenge, run is the solution.

This can be inverted. For instance (as will be seen below), the easiest and most accurate way to measure grade is to measure out a set horizontal distance, and then the grade is proportional to the measured vertical rise.

Grade can be measured directly as an angle, but without diving into trigonometry (i.e., having basic trig skills and packing a calculator, or possibly a slide-rule) all we can do with an angle is compare it with another angle. That tells us nothing about how long a traverse needs to be extended (see example), nor the overall ("average") grade around a turn.3

There are also differences in how horizontal and vertical distances are measured. Horizontal distances of a hundred feet (or more) are easily and accurately measured with a suitable measuring tape. Vertically, though, we are rather constrained to how far we can reach, which for most people is around seven feet (about two meters). But the big problem is that the endpoints of what we want to measure vertically are often separated horizontally – perhaps by a hundred feet, or more. Another problem is that in the range of grades we are interested in the vertical value is more sensitive to error than the horizontal value. Fortunately there are simple methods for measuring rise as well as run.

The key to measuring the rise between two points is to determine a common datum, or horizontal reference line, between them. It is then (mostly) a simple matter to measure the differences between the datum and the points on the ground at each end. Given that horizontal reference, all of the methods to be described below are just different ways of measuring the vertical differences.


Tools.

The gold standard for determining the vertical datum is with some form of a surveyor's transit. However, a transit, along with the tripod to mount it on, is bulky and cumbersome to carry, time consuming to set up, and very much overkill for the accuracy we need. (Surveyors commonly want accuracy of tenths of an inch in a hundred feet; we are good with an inch in twenty feet.) If you need to make measurements for some kind of structure, or will be making many measurements from one location, then it may be useful to use a transit. Otherwise, we need something simpler.

(I am occasionally asked about using GPS for trail work. Sorry, no. While it is true that geophysicists use GPS to measure tectonic movements of less than an inch, they use fixed stations, heavy wizardry, and equipment and data not available to the public. Consumer grade GPS is especially lame measuring elevation – read about "ellipsoid geoid separation" – and is often off by fifty to a hundred feet, or more. GPS is good for getting approximate location of trail or other features, but is entirely too coarse for trail work.)

Leveling scope.

Pole marked in inches. [pole1b-40.gif 40 KB]
Leveling scope. [scope1.jpg 16 KB]

The method recommended here for determining a horizontal line is to use a leveling scope. These are handy, inexpensive, and simple devices, yet fully capable of the accuracy needed for trail work. There are several types; the one pictured here is a standard design that has been sold for at least a half-century, and is available under various labels. Leveling scopes are similar to clinometers (which we won't consider, for reasons previously discussed in Grade) in that you sight through them at a target while holding a bubble in alignment with an internal marker. The big difference is that clinometers try to measure a range of angles, which for the pocket variety leads to a trade-off with precision, whereas leveling scopes measure only one angle, the horizontal.

Poles.

A pair of poles is also needed. With just a little bit of work suitable poles can be made from a ten-foot length of half-inch diameter PVC pipe, available at any hardware store. At a minimum this should be cut into two five-foot pieces.4 These are not too much to carry in hand, but for a handier, more compact version that can be packed cut each pole into three 20 inch pieces. (Or four 15 inch pieces.) Glue a coupling (also available at the hardware store) on the end of two of the three pieces, and they can be fitted together for a complete pole.5

The complete pole is marked with indelible pen at every inch6, and labelled from 1 to 60 (from the top down; see picture). Write the numbers as large and clear as possible. A band of red tape at each end is also good.7

A suitable target is also needed. In a pinch almost anything can be used, but something bright, about two inches by five inches, works better. I found some bright pink, translucent plastic that has worked very well. (Translucence is very nice when there is light on the back side of the target.) And carry spares, as they do tend to get lost. 8

Tape measure.

For measuring horizontal distances two items are needed: First, a a self-retracting 25' tape measure that counts inches all the way to 300. (And in a bright yellow or orange case, so you can see it in the bushes.) Second, a 100' fiberglass (or similar) tape measure. This should not be metal, as metal is too prone to being bent or kinked. The common 300' open-reel tape measures can work, but the more compact 100' tapes in a closed-reel are handier to pack. Mark every hundred inches with a solid red mark.9

If a project should extend for a quarter of mile or more, a wheel is recommended for measuring distance (and establishing 'stations', described below). This is not needed for smaller projects and individual turns as are described here.

Pencil level.

Pencil level. [level1-2.gif 15 KB]

It is very handy to have a pencil level. Sometimes labelled "pocket levels", I do mean the levels that are about the size of a large pencil (the one pictured is five inches long), and come with a clip so they can be securely and conveniently kept in a shirt pocket. Checking grade or outslope with a pencil level and tape measure is so easy (once you learn the trick, coming up) that I think it is tantamount to negligence for trail builders to not carry – and use – a pencil level and tape measure.

Miscellaneous.

String can also be very handy, especially for checking grade. Get nylon string, which is strong, resistant to the ravages of wet, and has just enough stretchiness that it can be pulled up tight. I have found it useful to have a length of just over a hundred feet, which does present a storage problem. One solution is to a make a spindle out of a piece of wood or plastic like a paint mixing stick. A little bulkier but perhaps better is to get an enclosed reel like carpenters use for chalk lines (but without the chalk). Some additional uses for string will be encountered later. Note that twisted nylon string immediately starts unraveling when the end is cut; it is best "cut" by burning through with a match.

Experience will quickly suggest various miscellaneous items needed. Like indelible pens (carry spares, especially in wet weather) for marking ribbon and stakes, a pocket-size notepad for taking notes, perhaps a bigger notebook (and clipboard) for taking more extensive notes and sketches, small plastic bags to keep the notepads dry, and multiple pencils (get the cheap but bright orange plastic mechanical pencils). A couple of roofing nails for nailing a target to a tree is one way of establishing a datum for future reference. Most of this measurement work requires two persons, but if you have to make some measurements by yourself a foot long piece of half-inch diameter rebar stuck in the ground will work to hold up a pole. And if you won't have a grub hoe at hand you will want to take a hammer for pounding in stakes.

A six- or eight-inch plastic slide-rule can also be handy – if you can find one. (Not the good quality plastic, but the cheap, flexible stuff that is less likely to break in your pack).

For reconnaissance work it is adequate to hang plastic flagging every fifty or hundred feet or so from any convenient branch. Construction of grade requires finer control, so we use pin flags: squares of plastic on a length of wire. These come in various sizes and colors. For marking the flag line (and outside edge of the bench) I recommend the smaller 2"x2" square flags, in yellow or pink. For special points I use red and orange, perhaps in a larger size. Dark blue is harder to see at any distance, but is fine for marking the start and end points of walls and other structures. Not that you need to purchase a bunch of different colors. Just get a bundle or two of yellow or pink flags, and then pick up a few other colors by swapping with other trail builders. If you are working on rock the pin flags won't work; you will want some carpenter's crayon, or "keel", and possibly a can of spray paint (get the kind for inverted use).

At any place where the grade is critical – like the turn of a switchback – you should use survey stakes to mark elevations. Get the four-foot long stakes, available at any construction supply store. Or check with your local land-manager, as they often have them.


Methods.

Horizontal measurement.

The method by which grade is measured will depend on the intended purpose, conditions, skill of the personnel, and whether one is taking a measurement, or laying off a measurement. The former is finding the measurement of something (and presumably recording it); the latter is using or applying a measurement. For instance, measurements might be taken of an existing turn to find out how steep it is. After calculating how far it has to be extended measurements would be laid off to show where the new turn should be built. Flags, stakes, or other marks are used to mark where measurements should be taken, have been taken, or where work is to be done.

It is not possible to describe every possible situation; I will describe several representative usages and methods, which the reader should adapt as needed. This warrants emphasizing: in particular cases you will undoubtably have to adapt the general principles and methods demonstrated by these specific examples.

Grade is the proportion of rise over run; the measurement of grade is the measurement of rise and run. The measurement of run – the horizontal component – is trivial, and only two points are worth mentioning. The first point is regarding making the measurement on the slope – that is, measuring the hypotenuse of the slope (or grade) triangle rather than the base. Such a measurement would be longer than the true horizontal run, but for grades under 30% the difference is so small it can be ignored. For steeper grades the tape should be held approximately level, which may require breaking the measurement into shorter lengths.

Stationing.

The second point is the method of stationing. When a long interval is to be measured it can be tedious, as well as difficult and erratic, to have to measure everything from the start, which might be at a considerable distance through difficult ground. Surveyors solve this by establishing stations at fixed distances, typically every one hundred feet. Once the stations are determined every intermediate interval is measured relative to the last station; no reference to any other location is needed, or even desirable. This is especially useful in trail work, where no two persons, nor even a single person any two times, will ever trace identical paths through the twists and random vagueness of real trail.

At the commencement of any trail work – and I do not refer to actual construction, but to the preliminary measurements – it is useful to establish stationing. Start by locating a reference mark – such as a knob of bedrock, or a target nailed to a stump – and mark it. For a longer project (such as a quarter mile or more of switchbacks to be blasted out of rock) use a wheel to set stations every hundred feet. For shorter projects (such as individual turns, or traverses of a couple hundred feet) set stations every hundred inches (for reasons to be explained later) using the 100' tape measure. Use stakes or pin flags. If they might be disturbed or vandalized, mark the location of each with a spot of spray paint. It may be useful to also record distances to various features for future reference.

There is a special way of referencing locations with stationing. Each station – whether a hundred feet, or a hundred inches – is numbered consecutively: 0 (at the origin), 1, 2, 3, etc. Intermediate intervals are appended, using a plus sign, as offsets from the last station. (Not to be confused with the offset mark to grade on a grade stake.) E.g., 3+52 is 52 feet (or inches) past station 3, which is nominally 300 feet (inches) from the origin. Note that it is invalid to say that location 3+52 is 352 feet (or inches) from the origin. The +52 offset is relative to station 3, nothing more. The actual distance might change if, for instance, the line was shortened (or lengthened) around station 2, but 3+52 still refers to a distance (52) relative to the last station (3). Stations are typically written at the top of a stake; the plus sign is often left off, and the offset written like a superscript, and possibly underlined: 352. At the stations the "00" offset might even be left off, leaving just the bar: 3–.

Vertical measurement.

The measurement of rise – the vertical component – is trickier, but is basically simple, and the basics can be learned in just a few minutes. The key, of course, is establishing the horizontal line, or vertical datum, between the two points of interest; this is done with the leveling scope. This can be done in various ways, but here we will look at only the simplest situation: the scope is placed on top of a pole (which serves as a monopod, in lieu of a tripod) at the lower of the points to be measured, and sighted toward the other pole (serving as a surveyor's rod). The horizontal line from the top of the lower pole will intercept the upper pole at some below its top, which (assuming the poles are the same length) is the rise between the two points.

While looking through the leveling scope a horizontal or "level" line is established when the bubble bisects the horizon line. (Often there is more than one line, but this will be the one in the center.) While holding this position the line of sight is extended to the distant target. An error that novices commonly make at this point is to look through the scope at the distant target, and then try to bring the bubble and horizon line into alignment with the target. Wrong! Establish the alignment of bubble and horizon line first. Then, while holding this alignment, look towards the distant pole, and have the "rod man" 10 move the target until it is in alignment. This is the key to accurate measurement of rise (also applies to using clinometers, which we are not), and may require some practice.11

Once the level line is established the rod man is directed to move the target ("big up", "big down", "little bit up", etc.) until the top edge of the target is at the line of sight. At that point the scope man (scoper?) calls out "mark"; the rod man then clamps the card to the pole so it won't slip, and then reads off the number above the target. 12

What happens after this depends on the purpose for which the grade is being measured.

A long grade.

If the purpose is to measure and record the grade on a long ascent, then there will be a person designated as a recorder (possibly a third person, else the scope man) who writes down the measurement, and then calls it out for confirmation. The scope man will then move up to where the rod man is, and place his pole exactly where the other rod was, and the rod man will proceed to a new location. Note that at each location the rod man should scrape of any vegetation and loose soil and stamp down a small platform for the pole. When doing a series of measurements like this it is very important that there be a definite spot, so that each measurement starts from exactly the same place where the prior measurement reached.

If the points being measured are well marked then it is feasible, and sometimes more convenient, to do just the leveling (taking the elevations) on one pass, and take the horizontal measurements on a different pass. Otherwise they should be taken at the same time as the vertical measurements. Note that measurement of rise does not require following the same route as measuring the run; the difference of elevation between two points is (or should be!) the same regardless of what route is taken.

So what do you do with these measurements of rise and run? Recall the definition of grade: it is the ratio rise over run. Here again is the equation that demonstrated this:
Equation for calculating grade.  [grade20.gif 4 KB]

That looks simple enough, but real life does not turn up such easy numbers. More likely you will have data like 11 feet of rise in 73 feet of run. What is the grade? Well, in the example above measurements are being taken, and recorded, for later use. So it is quite feasible, and even recommended, to input them into a spreadsheet, and let the computer do the drudge work.

Magic trick.

But what if you are taking a measurement for immediate use (perhaps to check on the work), or need to lay off a grade – then what? I do not recommend a calculator (not rugged enough for trail conditions, and too much button pushing), and slide-rules are not easily found. But here is a neat trick: note that grade is a percentage (from the Latin per centum, or "for each hundred"), and in fractional form would have 100 as the denominator. So if you need the grade of a short bit of traverse, just select two points 100 inches apart; the inches of rise are numerically the same as the grade. This is why you want to memorize the magic number of 8' 4". Why is it magic? Because it is 100", and makes division disappear! Also keep in mind the magic of 25' = 300".

Of course, there will be times when the data is not so obliging. At such times a slide-rule works great. Or just use pencil and paper to work out the answer. This is not needed too often, so the time and effort is not too great.

Out-slope.

Measuring out-slope. [outslope1.jpg 41 KB]

This gets better. I usually have a stake (a straight one) with a mark at either 33 or 25 inches from the end. To measure out-slope extend the tape four or five inches, lay it across the stake at the mark, and clamp it with your thumb. Rest the end of the stake on the high side of the slope, use your other hand to rest the pencil level on the edge of the stake, then let the stake slip down the tape until it is level. Clamp the tape, then pick it up and read the measurement (to the bottom of the stake). The result is one-third (or one-fourth) of the value that would be obtained if the rise of this slope was measured across 100". Just multiply by three (or four), and you have the grade. Voilà!

Width:   24"    36"    48"    60" 
        ----   ----   ----   ---- 
 2%     0.5"   0.7"   1.0"   1.2" 
 4%     1.0"   1.4"   2.0"   2.4" 
 6%     1.5"   2.1"   2.9"   3.6" 

While we are on the topic of out-sloping let's consider just how much outslope is needed. The general recommendation for out-slope (or in-slope) is from 2 to 6 percent – enough to shed water off the tread even with a slight trough, but not so much as to tend to turn ankles. Often this is specified as "about two inches" of rise. But that is only part of the story: it also depends on the run, in this case the width of the tread. The table shows the amount of rise (or fall) across the full width of the tread for various amounts of outslope. Taking the middle value (4%), note that 2" is fine for a four-foot wide tread but at the high end for a three-foot tread; a two-foot wide tread might be better with only an inch of rise across the full width of the tread. This is too subtle to do by eye alone, even by experienced trail builders, which is why you should always measure it!

Quick grade.

Here's a variation: For a quick measurement of grade, extend a tape out horizontally 50 inches with the end on the tread and the 50" mark against your leg. Put the pencil level in the hollow of the tape measure and raise or lower the tape until level. Grab the level, then put a finger on your leg at the tape measure. Retract it, then measure from your finger to the ground. Since the run was only half a hundred, multiply the result by two to get the grade. (This is a quick and excellent way of sampling grade on the run, but keep in mind that it is only a sample, and is subject to error if extrapolated.13)

Laying off grade on the run.

Here is another neat trick, and an example of laying off a grade. Take a piece of nylon string about ten feet long, tie a loop about two inches long in one end. Measure off 102" (need a couple extra inches here), fold the string back to form a loop about two inches long, and tie it off. (Not too tightly yet, as you may need to make some adjustment.) Put a pole in each loop, and check that they are 100" apart (else adjust).

Assume that you want to lay off a grade of, say, 12% for a new trail across an uncomplicated slope of some 200 feet across. How can you do this simply and quickly?

Put a pole into each loop of your magical 100" inch string, and put the first pole at the starting point (presumably at the bottom of the grade). The rod man takes the second pole out to the end of its leash – 100" – in the proper direction, and approximately 12" higher. She (why not?) then uses her boot heel to scrape away any vegetation, duff, and loose soil at that point, and places the rod. Shoot the horizontal line and take the rise. It is probably a little more or a little less than 12". The rod man takes the difference and adjusts the rod. Reshoot the line and check the rise. If it is correct, the rod man sticks in a pin flag. Scope man and rod man move up until the scope man is on location (taking care to place the pole exactly where the other pole was), and the process is repeated.14

Flagging.

In the example above the pin flags (and possibly stakes) mark the outside edge of the bench the tread will be constructed on. There are other possibilities (center line of the trail, inside edge, top of cut-slope, bottom of fill-slope), and typical practice for surveying a road or railway is to stake all of them. This is overkill for trail work, but there is some division of opinion within the trail building community as to where the flagging should go. I will discuss this further in Flagging, but for now I will simply state that flagging and staking should generally be done at the outside edge of the bench.

Vertical Control and Staking.

It may be recalled that some definitions of switchbacks characterize them as having "alternate sharp ascents and descents", like a roller coaster. If you do not carefully control elevation at every point – what is called vertical control – that is just what you might get: a roller coaster. (Well, somewhat like a roller coaster.) For vertical control you need stakes, with the proper elevation marked on each.

Grade stake with tread cross-section. [gradestake-2.gif
16 KB]

Assume that you are to construct tread between two end points whose overall rise and run are known, and acceptable. Starting from the bottom, put a stake every 100", with proper station marking. These should be six to ten inches beyond the estimated outside edge, to avoid being disturbed by construction. Part of the task here is mark each stake with a grade mark showing the desired elevation of the grade. This is a special mark, a zero with the horizontal mark or bar through the center. (Much like the mark accountants use when they don't want to write out a whole string of zeros.) Now working at grade level – which at places may even be below the ground surface – can be difficult. So we typically add offset marks 12 or 16 inches (sometimes more) above the grade mark. These have the offset (such as "+12" or "+16") written above the mark. (See diagram.)

So how do you determine where these marks should be? If the section is not too long you can simply determine the offset at each end, and stretch the string between them. (Tightly, so it doesn't sag. Check by looking up the string.) The string is where the offset mark should be; measure down the indicated distance for the grade mark.

Otherwise you can use the scope. Several methods are possible, but here is one for when doing this alone. Set a pole next to the first stake down from the top. Use the scope to get the level line from the offset mark on the top stake (you might need to tie a bit of ribbon just below the mark to make it more visible), note the position on the pole. Subtract the appropriate rise, and you have the offset mark for this stake. Proceed to the next stake and repeat. If the rise on the last section doesn't work out quite right, you might check using a string, or by the method described next.

A very handy technique here is to bend the end of a pin flag so it can be clipped onto the stake, and hung out over the bench (as shown in the diagram). (You will need pliers to bend the wire, and the pencil level to ensure the flag is horizontal.) This is handy in two ways. First, once you have hung and leveled all the flags, you can sight along them (as with the string) to see if any are misaligned. Second, it is quite difficult to ascertain elevation by eye, especially when looking down. But it is trivial to measure down from the flag. Since tape measures are a relatively scarce item, I usually mark some of the tool handles every four inches. Your diggers, even the neophytes, can readily tell if they are close to grade by comparing the height of the flag with the marks on the tool. These flags will get bumped, but with the pencil level they can be readily restored to the proper position.

Turns.

All of the previous examples have assumed a fairly straight traverse. Staking a curve is a little more complicated, which I will discuss in the section on Flagging. The key thing to remember in measuring the grade or length of a turn is this: always measure the grade of a turn on the inside!


Summary.

The fundamental basis for respecting grade is simple: measure it! Grade is the proportion of rise over run; the measurement of grade is the measurement of rise and run. This can be done easily, quickly, and with sufficient accuracy using simple tools and methods as described above. The key concept is to use a leveling scope to establish a vertical datum between the points being measured. And don't forget why 8' 4" and 25' are magical.

Back to Grade.

Back to Switchback Theory and Principles.


Notes.

  1. The tools and methods described here I have worked out by experience, by experimentation (with the assistance of a colleague who wishes to remain anonymous), and study of the methods of surveying. Surveying, which is the definitive science and practice of measurement, tends to be overkill for trail use. I suspect that, and the lack of any alternatives heretofore, may be why trail builders have generally disdained any kind of measurement. Real surveyors will undoubtably sniff at the methods described here, and perhaps have issues with some of what I present. However, it should be kept in mind that 1) the focus here is on what is suitable for trail work, and that 2) even approximate measurements are better than no measurement at all. This is an initial try, a first approximation, with all the short-comings and blemishes of such. I will be pleased if in ten or fifteen years the principle of "measure it!" has become widely accepted, and sufficient experience has been collected for a better formulation of these methods.
  2. The possible routes that stay reasonably close to the topographic surface are relatively less, but still infinite in their variety.
  3. Direct measurement of the angle between any two points on a turn gives you the "grade" of the shortcut along the line of sight. The grade of the turn depends on the length (run) of the turn, which is independent of the topographic distance or angle between the end points.
  4. The length of the pole determines the height at which the scope will be used. Five feet (60") is convenient computationally, and for anyone at least 5' 5" tall. Shorter persons may need to use 48" poles.
  5. The couplings leave a little gap between the pieces, so the other end of the piece needs to be filed down a tad to keep the length right. This needs to be done correctly, and uniformly, on all pieces. It is best to set up a simple jig with a spare piece of PVC cut exactly to some multiple of inches. Slip the jig into the coupling end, and the other end of the piece should be filed down until it is exactly twenty inches plus the length of the jig. To file accurately it is best to clamp the piece in a vise, or to a railing, or some such.
  6. Everyone outside of the U.S.A (and Burma and Liberia) will be using the metric system. The principles described here still apply, but 254 centimeters (the equivalent of 100 inches) is not handy, and 100 cm (1 meter, or approximately 39 inches) is generally too short. Perhaps 200 cm is convenient (remember to divide the measured rise by two to get the percent grade). I advise against a straightforward conversion of all measurements here into millimeter equivalents (as the USFS is wont to do). The utility of the methods described here is due in part to computational simplicity, and particularly on use of lengths whose numerical value (in the denominator) is multiples of 100. True metrification is learning how to work with suitable metric values, not mindless conversion of inherently English values into uselessly precise metric equivalents.
  7. You might think you are sighting on the very bottom of a pole resting on the soil, but how would you know that an inch or two is not buried in the soil? By the red band.
  8. The classic surveyor's target is a small card with alternate white and red (or orange) quadrants, with the intersection at the center being the point aimed at. However, I find that my helpers often find this confusing. So for trail work I recommend consistently using the top edge of the card.
  9. I would have liked a 100' tape marked in inches all the way out, but they don't seem to be made. It is easy enough to keep track of every 300" (25'), and with enough practice even the intermediate values (8' 4", 16" 8", ...) will become familiar. But best to mark the tape every hundred inches to avoid error.
       Also be careful to get a tape with the feet subdivided into inches, not tenths of a foot.
  10. Yes, women can do this, and even little girls (if they can reach high enough), and all very well. The term "rod man" has a long precedent in surveying in referring to a particular and well-defined position, and is not as cumbersome as alternative terms. Use of this and other "masculine" terms is in no way meant to be gender restrictive.
  11. Practice is good. Try this: On two posts about fifty feet apart fasten targets, but not at the same height. From one post look through the scope and establish the horizontal (level) line. Raise or lower the scope until the target comes into alignment, then mark the height of the scope with a pencil. Do this a few times, and see if the pencil marks are clustered together. Repeat from the other post. Then measure the distance between the pencil marks and the targets; this should be same at each end. Practice until they are. Note that this establishes precision (which is good), not accuracy (see any statistics book), but accuracy requires precision.
       Accuracy depends on both operator and the scope; this can quickly get beyond the scope of this discussion. (Best to not mess with the factory adjustment.) But if you need to check your accuracy, and do not have a real surveyor to assist, try this: Do the first part of the previous exercise, and if you have a tight cluster of marks use them to mount the second target at this putative level line. Then do the second part of the exercise. If both instrument and operator are accurate then the second set of marks should be at the same height as the first target.
       Note that even if the instrument is accurate, any variation is an error. If in the field you do not take each measurement multiple times and average, the effective accuracy will be no better than your precision. To improve accuracy you must first improve precision.
  12. We are looking for accuracy of only an inch, but strictly speaking this requires measuring at a precision of half an inch. There is also the matter of the line of sight of the scope sitting half an inch above the rod. I have not worked out the details of optimal practice; so far it seems adequate to ignore the fractions of an inch, and the half-inch at top. This bears more study and experience.
  13. The scale (the length of the measurement) is important. A long scale – like, say, the entire 650 foot length of a traverse – would miss all the little dips that can so easily erode into potholes. And a short scale, while correctly reporting the grade at that point, can be extrapolated to a longer scale only to the extent that the overall length is straight and flat, and the short section is truly representative. Different methods of measurement have different limits, and it is important that the method be appropriate for its intended use.
  14. This can be done going downhill, though the way this method works the scope man has to be on the downhill end. It may be tempting to have the rod man could just hold the target at the proper mark and let the scope man do all the adjustments. But this could lead to unconscious biasing. It is generally best to have the scope man make the subjective decision as to where the mark is "blind"; that is, without knowing the value until after the mark is made. (This is one reason why clinometers are suspect: bubbles are too often sympathetic to disappointment.)

Copyright (C) 2008 by J. Johnson.