Vertical angle calibration of a theodolite

Poloko Kuduntwane

27/09/016

Test and Measurements Conference 2016

Background

• As NMISA there is a need to calibrate specialized equipment and artefacts mainly used for calibrating the vertical angles of theodolites in the industry, with an accuracy of 0.2 arc sec. Horizontal angles are currently calibrated.

Collimator at 30 deg

Collimator at 0 deg

Collimator at -30 deg

Contents

• General calibration methods found on literature• Theodolite Errors• NMISA proposed calibration methods for investigation• Project Results

Introduction

1. Solid angular gauge method using polygons (multiangular prisms)

General Angle Calibration Methods

Applications of these methods

2. Trigonometric method (angle determination by means of linear measurements)

3. Goniometric method (plane angle determination by means of a circular scale)

21 3

Theodolite Errors

• Trunnion axis is not perpendicular to the vertical axis

• Line of sight is not perpendicular to the trunnion axis

• Vertical axis is not plumb

• The vertical angle collimation is out of adjustment

Two NMISA Proposed Vertical Angle Calibration Methods

Method 1: Solid angular gauge method using polygons

• This method uses an auto-collimator against a 12 faces precision polygon with the pitch of the angle measurements (due to the angle between faces) of 30˚

• The disadvantage of this method is that it can only check a few number of values or angles

NMISA proposed calibration method/setup

• The polygon was attached to the theodolite telescope through a special aluminium shaft, which allows the telescope to rotate in conjunction with the polygon

PolygonAutocollimator

Aluminium Shaft

Polygon

Method 2: Trigonometric method (angle determination by means of linear measurements)

• Proposed method is based on a comparison of the angle measured by the theodolite and the reference angle determined by measuring two distances – the horizontal (the distance between the theodolite vertical axis and the vertically positioned target) and the vertical (the distance between the target and the vertically positioned reference EDM)

• Because it is difficult to measure the distance l from the rotation axis of the theodolite telescope, the vertical bar with the target is displaced and the target is also displaced upwards until it is in the centre of the telescope reticle. The new reference angle can be expressed as:

φ′ = arctan(∆ ℎ′

∆ 𝑙′)

where ∆ℎ′ - the known calibrated vertical distance of the displaced target and ∆𝑙′ - the known calibrated horizontal distance of the displaced vertical bar.

NMISA Clinometer Used For Comparing Results

Clinometer

Theodolite

Experimental Results (Method 1)

Averages and deviations from 5 measurements (Serial number: 1)

Nominal Angle

(deg)

Measured Angle

Theodolite

(deg)

Deviation

Theodolite

(deg)

Measured Angle

Clinometer

(deg)

Deviation

Clinometer

(deg)

30 133,3128 3,3128 29,254 0,746

0 100,0004 0,0004 0,704 0,704

-30 66,6469 3,3530 -30,698 0,698

Averages and deviations from 5 measurements (Serial number: DAST 9434)

Nominal Angle

(deg)

Measured Angle

Theodolite

(deg)

Deviation

Theodolite

(deg)

Measured Angle

Clinometer

(deg)

Deviation

Clinometer

(deg)

30 133,3093 3,3093 30,484 0,484

0 100,0003 0,0003 0,530 0,530

-30 66,6140 3,3859 -29,494 0,506

Experimental Results (Method 2)

Averages and deviations from three measurements (Serial number: 1)

Nominal Angle

(deg)

Measured

Angle

(deg)

Deviation

(deg)

30 133,6175 3,6175

0 100,0003 0,0003

-30 66,9825 3,0175

Averages and deviations from three measurements (Serial number: DAST 9434)

Nominal Angle

(deg)

Measured

Angle

(deg)

Deviation

(deg)

30 133,3980 3,3980

0 100,0004 0,0004

-30 66,5219 3,4781

Conclusions

• The two methods’ results are in agreement with each other.

• The deviations of the average values from the nominal values is too big i.e. around 3.5 degrees for both the methods and both the theodolites, even though the repeatability of the measurement is good.

• This inaccuracy of the theodolites might be caused by the mounting of the attachment shaft for the polygon, which might have tampered with the angle-encoder/scale inside the theodolites.

• Another reason might be that the theodolites were simply inaccurate due to the previously discussed theodolite errors, as the measurements with Fujiyama Totalstation were better, within arc-seconds and minutes accurate.

• With method 2, there were many alignment challenges. The vertical distances from the base reference to the target, were measured by the EDM on a flat plane of the target. The flatness of this plane was also unknown.

• The vertical axis of the theodolite and its telescope could have not been parallel with the vertical axis of the vertical bar which the target is been adjusted on.

• The next step is to repeat the measurements with a new and high accuracy theodolite.

QUESTIONS???

The End