The Level

The objective of any leveling instrument is to direct the line of sight in a horizontal direction. The various models have different means of approaching this objective. Most levels are capable of turning only on a vertical axis. If that axis is plumb, and the line of sight is perpendicular to the axis, then the locus of the line of sight is a horizontal plane.

Axis Error

Having a plumb axis is more important for certain instruments than for others. The automatic level is the most prevalent type in use these days. It has an internal pendulum compensator, which adjusts the line of sight each time the instrument is moved. This mechanism fixes the line of sight to a constant angle with relation to the gravity vector, not with relation to the vertical axis. Because of this, the axis needs only to be close enough to the vertical to allow the pendulum to swing freely.

The tilting level, although less common, shares this same advantage. Each time the instrument is moved, the line of sight is manually leveled with a tube vial. The axis needs only to be roughly plumb.

There are other level models (e.g., dumpy) that have the line of sight set at a right angle to the vertical axis. For these models, properly adjusted level vials and strict attention to instrument leveling procedures are crucial.

Crosshair Alignment and Balance

The horizontal position of the crosshair is not important in a level, but if it is out of alignment vertically, it will cause the line of sight to dip or rise. In either case, the locus of the line of sight will become a cone rather than a plane. Assuming a flat Earth, the error on any given sight is in direct variation with the sight distance.

All instruments are in error, so turn the error against itself by balancing shots. In a level circuit with no inverted rod shots, backsight readings are added and foresights are subtracted. Therefore, if the backsight and foresight distances are equal, each backsight error will be canceled by the following foresight error. A rodman should pace the distance as he walks forward to the instrument, then pace the same distance forward to the next turning point. If it is not possible to set a turning point there, he should keep track of the balance. For example, if a foresight is 30 feet heavy, then the next foresight should be 30 feet light.

On steep ground, things can get out of hand in a hurry, especially if the instrument operator is not cooperating. Going uphill, and looking at a long rod, the gunner may be able to walk 200 feet ahead of the rodman before climbing above the top of the rod. When the rodman moves ahead, he may have to stop at only 70 feet because the ground is rising above the instrument. Now the foresight is 130 feet light on a single setup, and since they are still moving uphill, it will only get worse on the next turn. The gunner needs to shorten the backsights. The rodman might otherwise keep track of the balance and compensate on another part of the circuit, when they are moving on level ground or downhill.

The Peg Check

The peg check is a procedure for finding the vertical error in the alignment of the crosshair. Two variations are presented here. It is assumed that the line of sight is at a fixed angle to the gravity vector. With an automatic level or tilting level, this is a fair assumption. Otherwise, first do what is necessary to plumb the vertical axis.

There are certain measures that should be taken no matter what version of the peg check is used. The party member running the instrument should be the one with the best eyesight. Usually that will not be the most senior member, so set pride aside. This is best done in fair weather, preferably on a cloudy day. Do it on level ground, and use the best rod available. If the rod is in sections, arrange for all of the readings to be taken from the same section, negating any error from loose joints or an improperly fitted face. If a parallel plate micrometer is available, use it. If the rod is graduated in hundredths of feet, estimate the thousandths. Paced distances are good enough for all but the highest order work, but have one person do all of the pacing. Stadia distances might also be used.

Center-End Method

The center-end peg check seems to be the most prevalent, perhaps because it is the easiest to learn and understand. It begins with two pegs (A and B) set about 300 feet apart, and the instrument dead center between them. Give peg A an arbitrary elevation. Backsight A and foresight B. Since the shots are in balance, this should give the correct difference in elevation, even if the instrument is in error.

The instrument is then carried toward peg B and set up very close to it, just outside the minimum focus distance. Backsight B and close the loop back on A. The loop is now heavy on the foresight. If the measured elevation of A is too low, then the line of sight is rising. If it is too high, then the line of sight is dipping. All of the error is on the back run.

If the error is out of tolerance, leave the instrument in the same position and make the adjustment with the long foresight. At this point, many instrument operators simply adjust the crosshair up or down by the amount of the closure error. That is close, but geometrically incorrect. The error is spread over the distance of the imbalance, but the foresight distance is somewhat longer than that. multiply the closure error by the ratio of the forsight distance to the imbalance. In the example used here, the loop is 270 feet heavy on the foresight and the final foresight is 285 feet. The correct adjustment is the closure error times 285/270.

End-End Method

With the end-end peg check, both setups are out of balance. This way it is possible to create a greater imbalance while using shorter sights. Set the pegs about 200 feet apart, and place the instrument very close to peg A and outside of the course. Take a short backsight on A and a long foresight on B. Move the instrument to a spot very close to B and outside the course. Backsight B and foresight A.

The correction adjustment for the end-end peg check has the same formula. Remember that the imbalance is twice the distance between the pegs. In the example above, the adjustment would be the closure error times 215/400.

Back to The Geometry of Surveying

Last update: January 26, 2012 ... Paul Kunkel whistling@whistleralley.com
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