The Nature of Measurement: Part 10: Achieving Accuracy in Distances

Many typical instrumental and natural errors in distance measurements are often misunderstood or overlooked. Being systematic in nature, such errors cannot be found by "closing" surveys because relative error of closure checks precision, not accuracy. If these errors are not removed, distances will be inaccurate.

Some of these errors are purely systematic. That is, they obey known mathematical or physical laws and generally change in proportion to the change in the condition causing the error. Others are constant and do not change with some variable condition. Still other errors are systematic in nature but random in effect. Such errors become randomly distributed in the survey. The first type of error will be simply called systematic, the second will be called constant and the third will be called quasi-systematic.

The errors to be discussed are the most common, but the list is by no means complete. I have not attempted to provide a thorough explanation of the testing and calibration procedures. The goal is to encourage achieving the highest practical accuracy in measurements.

Modern land surveying standards are starting to require distances or relative positions accurate to a few hundredths of a foot (depending on "class" of land and scope of survey). For example, Kentucky's new standards, which began to be enforced July 1, 1998, require distances to be accurate to 0.05 feet + 100 PPM (parts per million) in urban and suburban surveys. Washington's standard is more stringent, allowing a positional tolerance of 0.07 feet + 50 PPM for urban surveys. Oregon's standard requires positional accuracy of 0.10 feet or 1:10,000, whichever is greater. To achieve any particular positional accuracy, distances must be more accurate than the positional error allowed because direction error also contributes to the positional error.

To control systematic errors in electronically measured distances, the constant and scale error of the instrument must be determined by proper use of a 4-point base line, temperature and pressure errors must be controlled, reflector constants must be known and applied, tribrach optical plummets and prism pole circular bubbles must be kept adjusted and slope measurements must be properly reduced to horizontal. In many cases (for example, urban surveys), use of tripod mounted reflectors may be necessary in place of prism poles.

Natural Errors in EDM

As a "rule of thumb," an error of 1ºC in the air temperature causes about 1 PPM error in a light wave measurement. Similarly, an error of 0.1 inches in pressure affects the measured distance by 1 PPM, as does an elevation difference of 100 feet. Such errors are negligible for topographic surveys but can be significant for boundary surveys.

For example, suppose the field crews do not change the PPM variable in the total station during times when there are wide swings of temperature. If the temperature goes from 5ºC to 24ºC (41ºF to 75ºF) on a spring day, and the PPM correction was not changed from morning to afternoon, the field crew would have a discrepancy of 0.06 feet in a 3,000-foot distance at the two different points in time.

Atmospheric pressure can also change several tenths of an inch over a few hours when weather is unstable. A weather radio broadcasts the pressure at the weather observation station, which may be miles away from the job site, and the weather may be significantly different there, causing another discrepancy. Considering that 100 feet in elevation difference causes 0.1 inches pressure difference, surveyors working in hilly or mountainous areas have an additional problem of constantly watching the pressure as they change elevation.

The biggest oversight concerning pressure occurs when the field crew uses the cited pressure directly from the weather broadcast. This is not an error, but a mistake because the pressure cited is "sea level" rather than local. Because the pressure drops with altitude, approximately 0.1 inches per 100 feet of altitude above sea level must be subtracted from the sea level pressure. The 1,900-foot contour passes through my back yard. If I were surveying in this subdivision, I would probably start with the broadcast pressure, then subtract 0.1 times 19, or 1.9 inches from that for keying into the total station. Neglecting this difference would cause 19 PPM error in the distances. Thus, a distance of 3,000 feet would have an error from this source of 0.06 feet, the same amount caused by the 19ºC error. If such differences are cumulative, not compensatory, we have a total error of 0.12 feet as a result of overlooking two commonly misunderstood aspects of temperature and pressure.

Instrument Errors in EDM

Without getting into complicated electronic aspects, let us simply say that two errors are associated with the EDM measurement: a constant error and a scale (PPM) error. An electronic distance instrument can be easily calibrated to discover these corrections. When done, the errors in future measurements from these sources can be controlled within a few millimeters (a hundredth of a foot or so). However, the test must be carefully and properly made. As a general specification, I try to have not more than one millimeter error built into the test from any one source. That way, once several error sources become combined, I probably have an accurate calibration within a few millimeters.

The NGS (formerly Coast and Geodetic Survey) installed hundreds of EDM base lines throughout the United States during the last 25 years. Although many of the stations have been disturbed, many have been maintained and some have been remeasured. Generally the intervals between points are accurate to a few tenths of a millimeter. It isn't important to understand how these accuracies were accomplished. Suffice to say that the published intervals represent "truth" for the surveyor. The base lines consist of four marked monuments, all in a straight line over uniformly sloping terrain. Typically, they are called the "0," "150," "430" and "1,400" stations, the numbers representing the distance from the "0" point. The accurate values, both horizontal and "mark-to-mark" (slope), are published on the description sheets.

EDM Calibration

Those who remember how to calibrate a steel tape will recall that a tape is not magically its optimum at some textbook values for temperature and tension. The same holds for EDM. To have accurate distances with a tape, the surveyor must calibrate it—that is, stretch it across a base line of known and highly accurate distance and observe the reading on the tape markings. An EDM must be checked in a similar way. In the case of a tape, we must consider the temperature and tension. In the case of the EDM, we must consider the temperature and pressure. With a tape, we simply record the calibration temperature and tension. These become the "standardization" conditions. With a total station, we can render the effect of the natural errors negligible by keying the readings into the instrument. When calibrating an EDM in this way, the instrument test will result in a scale and constant error that is truly an instrument error, unaffected by temperature and pressure.

To avoid having an effect on distances of more than one millimeter, we can apply the above "rules of thumb" on temperature and pressure. Most EDM base lines have a full length of about 1,400 meters. Keeping the error from temperature under 1 millimeter for this distance translates to an allowable error of about 0.7ºC (1.3ºF) and 0.07 inches of Mercury. The second requirement when calibrating an EDM is to have tribrach optical plummets adjusted to within about 1 millimeter. The reflectors must be placed on tripods with adjusted tribrachs. A good calibration would be impossible using a hand-held prism pole.

Only one reflector should be used for an EDM calibration, and the reflector constant must be known and keyed into the instrument. Doing so compensates for this constant. Thus, the test yields only the instrument constant. If the reflector constant is set to "0" in the instrument, the test results in a "system constant" and is only good for use of the instrument with that particular reflector.

The minimum a surveyor can measure and resolve both the EDM constant and scale errors is three intervals (that is, measure the 150, the 430, and the 1,400 meter lengths). A better set of data, yielding better results, requires six intervals. For the typical 4-point line, these six lengths are 150, 280, 430, 970, 1,250 and 1,400 meters. These measurements are accomplished by an efficient program of moving the instrument and reflector, minimizing the set-ups. All the while, the temperature and pressure should be monitored. It is best to do the calibration on a day when these variables are predicted to be fairly constant and then work efficiently to complete all measurements.

It is advisable to make about 6 to 10 repetitions of each distance, using the mean of the set. You can use either the horizontal or slope distances, as long as you are consistent. A total station that automatically calculates the horizontal distance is best because there is no need to measure tripod heights. For older instruments that do not calculate horizontal distance automatically, setting the reflector at the same height as the EDM and using the slope distances is convenient. After the data is collected, a least squares fit (linear regression) is done to determine the constant and scale corrections. These numbers are used to correct future distances, the theory being the same as when using the calibration error of a tape to correct measured distances.

The main difference between tape and EDM corrections is the scale correction in the latter. The existence of the scale error creates the need for four points in the base line, the measuring of six intervals instead of just one and the linear regression calculations. The most common oversight of many surveyors is just to go out and check one interval along a base line. This is insufficient because it does not isolate the scale error from the constant error. If the constant error was small, the EDM readings might check the published base line lengths for short distances but will mysteriously begin to deviate as the distances become longer.

As an example, a total station was tested. The constant correction was 0.4 millimeters (essentially negligible), and the scale correction was 21.5 PPM. A field reading of 3,000.00 feet would have a "true value" equal to the reading plus the sum of the corrections, the basic equation of T = R + C being applied. The "R" is the observed EDM reading. The "C" is the sum of the two corrections. The constant correction (after making the units conversions) is 0.001 feet, and the scale correction amounts to 0.0645 feet, for a total correction of 0.066 feet. Thus, to the nearest hundredth, the accurate value T = 3,000.07 feet.

Other Systematic Errors

Optical plummets are more precise than plumb bobs but can be less accurate. Unless deflected, plumb lines by definition always point along the vertical and thus are "true." Optical plummets can easily become unadjusted. They can be checked and adjusted to within a millimeter or two. If the adjustment of the tribrach is uncertain, use of a plumb bob may be advisable.

Prism pole bubbles are another error source. Field crews should be taught to check the adjustment of rod bubbles frequently, using any one of several simple tests. Remember, these are precision instruments and as important for ultimate accuracy as the EDM instrument itself.

Reflector constants can vary a few millimeters from that cited by the manufacturer. The value can be determined to one or two millimeters by a simple test field.

Most land surveying distances are horizontal, not slope or geodetic. Unless the horizontal distance is computed in the total station, care must be taken that instrument and reflector heights are equalized so that slope distances are accurate. When attempting to project distances to a plane surface, other geometric errors exist because of the reality that the earth is round, not flat. When using state plane coordinates, for example, the scale and elevation factors must be carefully determined and applied.

It is a shame that some field crews probably check the oil level and tire pressure of the survey vehicle more often than they make accuracy checks of their surveying instruments. Modern survey standards cannot be achieved unless attention is paid to the errors outlined in this article. Alone, any one of the sources may be small and often insignificant. If enough errors are overlooked, accuracy may be far from what is desirable, and minimum accuracy standards may not be achieved, regardless of the precision indicated by traverse closure.

For more details of the various instrument test procedures, readers should contact the author.

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