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Sources of Error in Leveling

All leveling measurements are subject to three sources of error: (1) instrumental, (2) natural, and (3) personal.These are summarized in the subsections that follow.

Instrumental Errors

Line of Sight. As described in Section 4.15, a properly adjusted leveling instrument that employs a level vial should have its line of sight and level vial axis parallel. Then, with the bubble centered, a horizontal plane, rather than a conical surface, is generated as the telescope is revolved. Also, if the compensators of automatic levels are operating properly, they should always produce a truly horizontal line of sight. If these conditions are not met, a line of sight (or collimation) error exists, and serious errors in rod readings can result. These errors are systematic, but they are canceled in differential leveling if the horizontal lengths of plus and minus sights are kept equal. The error may be serious in going up or down a steep hill where all plus sights are longer or shorter than all minus sights, unless care is taken to run a zigzag line. The size of the collimation error, can be determined in a simple field procedure [see Equation (4.14) and Section 4.15.5]. If backsights and foresights cannot
be balanced, a correction for this error can be made.

To apply the collimation correction, the value of from Equation (4.14) is divided by the length of the spaces between adjacent stakes in Figure 4.20.This yields the collimation correction factor in units of feet per foot, or meters per meter. Then for any backsight or foresight, the correction to be subtracted from the rod reading is obtained by multiplying the length of the sight by this correction factor. As an example, suppose that the distance between stakes in Example 4.3 was 100 ft. Then the collimation correction factor is Suppose that a reading of 5.29 ft was obtained on a backsight of 200 ft length with this instrument. The corrected rod reading would then be 5.29 - (200 * 0.0001) = 5.27.

Cross hair Not Exactly Horizontal. Reading the rod near the center of the horizontal crosshair will eliminate or minimize this potential error.

Rod Not Correct Length. Inaccurate divisions on a rod cause errors in observed elevation differences similar to those resulting from incorrect markings on a measuring tape. Uniform wearing of the rod bottom makes HI values too large, but the effect is canceled when included in both plus and minus sights. Rod graduations should be checked by comparing them with those on a standardized tape.

Tripod Legs Loose. Tripod leg bolts that are too loose or too tight allow movement or strain that affects the instrument head. Loose metal tripod shoes cause unstable setups.

Natural Errors

Curvature of the Earth. As noted in Section 4.4, a level surface curves away from a horizontal plane at the rate of or which is about 0.7 ft/mi or 8 cm/km. The effect of curvature of the earth is to increase the rod reading. Equalizing lengths of plus and minus sights in differential leveling cancels the error due to this cause.

Refraction. Light rays coming from an object to the telescope are bent, making the line of sight a curve concave to the earth’s surface, which thereby decreases rod readings. Balancing the lengths of plus and minus sights usually eliminates errors due to refraction. However, large and sudden changes in atmospheric refraction may be important in precise work. Although, errors due to refraction tend to be random over a long period of time, they could be systematic on one day’s run.

Temperature Variations. Heat causes leveling rods to expand, but the effect is not important in ordinary leveling. If the level vial of a tilting level is heated, the liquid expands and the bubble shortens. This does not produce an error (although it may be inconvenient), unless one end of the tube is warmed more than the other, and the bubble therefore moves. Other parts of the instrument warp because of uneven heating, and this distortion affects the adjustment. Shading the level by means of a cover when carrying it, and by an umbrella when it is set up, will reduce or eliminate heat effects.These precautions are followed in precise leveling.
Air boiling or heat waves near the ground surface or adjacent to heated objects make the rod appear to wave and prevent accurate sighting. Raising the line of sight by high tripod setups, taking shorter sights, avoiding any that pass close to heat sources (such as buildings and stacks), and using the lower magnification of a variable-power eyepiece reduce the effect.

Wind. Strong wind causes the instrument to vibrate and makes the rod unsteady. Precise leveling should not be attempted on excessively windy days.

Settlement of the Instrument. Settlement of the instrument during the time between a plus sight reading and a minus sight makes the latter too small and therefore the recorded elevation of the next point too high. The error is cumulative in a series of setups on soft material.Therefore setups on spongy ground, blacktop, or ice should be avoided if possible, but if they are necessary, unusual care is required to reduce the resulting errors. This can include taking readings in quick order, using two rods and two observers to preclude walking around the instrument, and alternating the order of taking plus and minus sights. Additionally whenever possible, the instrument tripod’s legs can be set on long hubs that are driven to refusal in the soft material.

Settlement of a Turning Point. This condition causes an error similar to that resulting from settlement of the instrument. It can be avoided by selecting firm, solid turning points or, if none are available, using a steel turning pin set firmly in the ground. A railroad spike can also be used in most situations.