Attaining Precision with a Maximum Angular Error of Closure

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Attaining Precision with a Maximum Angular Error of Closure

You know that the sum of the interior angles of a closed traverse should theoretically equal the product of 180° (n – 2), n being the number of sides in the polygon described by the traverse. A prescribed MAXIMUM ANGULAR ERROR OF CLOSURE is stated in terms of the product of a given angular value times the square root of the number of interior angles in the traverse. Again, if we use the traverse shown in figure 13-27 as an example, the prescribed maximum angular error of closure in minutes is 01 fi because the figure has three interior angles. The sum of the interior angles should be 180°. If the sum of the angles as actually measured and recorded is 179°57´, the angular error of closure is 03´. The maximum permissible error of closure is the product of 01´ times the square root of 3, or about 1.73´. The prescribed maximum angular error of closure has therefore been exceeded.

Meeting Precision Specifications

The following specifications are intended to give you only a general idea of the typical precision requirements for various types of transit-tape surveys. When linear and angular errors of closure are specified, it is understood that a closed traverse is involved.

For many types of preliminary surveys and for land surveys, typical precision specifications may read as follows:

l Transit angles to nearest minute, measured once. Sights on range poles plumbed by eye. Tape leveled by eye, and standard tension estimated. No temperature or sag corrections. Slopes under 3 percent disregarded. Slopes over 3 percent measured by breaking chain or by chaining slope distance and applying calculated correction. Maximum angular error of closure in minutes is 1.5 . Maximum ratio linear error of closure, 1/1000. Pins or stakes set to nearest 0.1 ft. For most land surveys and highway location surveys, typical precision specifications may read as follows:

l Transit angles to nearest minute, measured once. Sights on range poles, plumbed carefully. Tape leveled by hand level, with standard tension by tensionometer or sag correction applied. Temperature correction applied if air temperature more than 15° different from standard (68°F). Slopes under 2 percent disregarded. Slopes over 2 percent measured by breaking chain or by applying approximate slope correction to slope distance. Pins or stakes set to nearest 0.05 ft. Maximum angular error of closure in minutes is ]. Maximum ratio linear error of closure, 1/3,000.

For important boundary surveys and extensive topographical surveys, typical precision specifications may read as follows:

. Transit angles by 1-rein transit, repeated four times. Sights taken on plumb lines or on range poles carefully plumbed. Temperature and slope corrections applied; tape leveled by level. Pins set to nearest 0.05 ft. Maximum angular error of closure in minutes is 0.5. Maximum ratio linear error of closure is 1/5,000.

Note that in the first two specifications, one-time angular measurement is considered sufficiently precise. Many surveyors, however, use two-line angular measurement customarily to maintain a constant check on mistakes.

Measuring Angles vs. Measuring Distances

It is usually the case on a transit-tape survey that the equipment for measuring angles is considerably more precise than the equipment for measuring linear distances. This fact leads many surveyors into a tendency to measure angles with great precision, while overlooking important errors in linear distance measurements.

Making the precision of angular measurement greater than that of linear measurement is useless because your angles are only as good as your linear distances. Suppose that you are running traverse line BC at a right deflection angle of 63°45´ from AB, 180.00 ft to station C. You set up at B, orient the telescope to AB extended, and turn exactly 63°45´00´´ to the right. But instead of measuring off 180.00 ft, you measure off 179.96 ft. Regardless of how precisely you turn all of the other angles in the traverse, every station will be dislocated because of the error in the linear measurement of BC.

Remember that angles and linear distances must be measured with the same precision.

IDENTIFYING ERRORS AND MISTAKES IN TRANSIT WORK

In transit work, errors are grouped into three general categories; namely, INSTRUMENTAL, NATURAL, and PERSONAL errors. First, we will discuss these errors, and then, later, we will explain the common mistakes in transit work.

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