WYLER AG, Inclination measuring systems Im Holderli 13, CH - 8405 WINTERTHUR (Switzerland) E-Mail: [email protected] Web: www.wylerag.com

Compendium inclination measurement WYLER AG, Winterthur / Switzerland Page General introduction to inclination measurement History of inclination measurement Units in inclination measurement Relationship between degrees/arcmin and µm/m Correlation between the most common units (SI) Correlation between the most common units in inclination measurement What are positive and negative inclinations? The absolute zero by means of a reversal measurement Effect of gravitational force and compensation with inclination measuring instruments Measuring uncertainty Length of measuring bases Absolute measurement...

Compendium inclination measurement WYLER AG, Winterthur / Switzerland 6.3

Compendium inclination measurement WYLER AG, Winterthur / Switzerland Preface There are already a great number of reference books on the topic of measuring techniques – so why the need for a book on inclination measuring technology? The title of this book “The Secrets of Inclination Measurement“ addresses the essential point: Inclination measurement holds a niche position within the field of metrology. The potential of this measuring technology remains largely unmet since it – and the implementation and interpretation of measurements for quality improvement – continue to be areas about which...

Compendium inclination measurement WYLER AG, Winterthur / Switzerland 1. General introduction to inclination measurement 1.1 History of inclination measurement Inclination measurement was used already in ancient times • for the construction of buildings • for the creation of simple city maps • for navigation at sea The use of new materials and working methods allowed the development of new and more accurate inclination measuring instruments • 1727 the first sextant was built according to Isaac Newton‘s designs • 1760 the first theodolite was made by the physicist Dollond Especially in the field...

Compendium inclination measurement WYLER AG, Winterthur / Switzerland 1.2 What is inclination? The expression “ANGLE“ is defined as the divergence between two straight lines g and g in a flat plane. The 1 2 angle d is created at the cross section between the two lines g and g . 1 INCLINATION is a specific, position-dependent angle whereas we distiguish between an absolute inclination and a relative inclination. The absolute inclination (illustration 2) corresponds to the angle a between the straight Illustration 1 line g3 and the horizontal straight line g4, whereas the horizontal line g lies...

Compendium inclination measurement WYLER AG, Winterthur / Switzerland 1.3 Units in inclination measurement For large inclinations from 5...10 degrees the following units are normally used: • • • • • • • x.xx Rad xxxx.xx mRad xxx.xxx° DEG xxx° xx‘ DEG xx° xx‘ xx“ DEG xxx.xxx GON xxxx.xx A%o radian milliradian degree degree / minutes degree / minutes / seconds gon artillerie-permille For smaller inclinations up to 5...10 degrees the following units are normally used: • • • • • • • • • • • xxx.xxx mm/m xx.xxxx “/10“ xx.xxxx “/12“ xxxx.xx mRad xxxx.xx µRad xxx.xxx mm/REL xx.xxxx “/REL xxxx.xx %o...

Compendium inclination measurement WYLER AG, Winterthur / Switzerland 1.5 What is a ^m/m? It is quite difficult to imagine an inclination of the size of 1 jm/m. Using a small mathematical relation it becomes more imaginable. By multiplying the baselength "L” and the height "h” by a factor of 1000, the relation remains the same, L = 1km and h = 1 mm (1 mm/km). This way, it is much easier to imagine an inclination of 1 jm/m. As an illustration, a human hair has a diameter of 50...70 pm. 1.6 What is a Radian? The radian is the standard unit of angular measure, used in many areas of mathematics....

Compendium inclination measurement WYLER AG, Winterthur / Switzerland 1.8 Correlation between the most common units in inclination measurement 1 Rad corresponds to 57.30° 1 mRad corresponds to 206.26 Arcsec 1 degree corresponds to approx. 17.45 mm/m or 17.45 mRad 1 Arcsec corresponds to approx. 4.85 µm/m 1.9 What are positive and negative inclinations? WYLER definition: An inclination is positive when the instrument, on that side on which an electrical connector is installed, is lifted. When the instrument under the same precondition is declined, we define this as a negative inclination. 1.10...

Compendium inclination measurement WYLER AG, Winterthur / Switzerland The word “linear“ comes from the Latin word linearis, which means created by lines. Usually, the term is used to describe a linear character. output measuring instrument Often, the basis between a measured quantity and the measurement signal (e.g. the output of the measuring instrument or the voltage of a sensor) is a linear function. The aim for a measuring device is proportionality and a small error of linearity. nominal characteristic maximum error of linearity Linearity according to DIN 2276: Measured value below half the...

Compendium inclination measurement WYLER AG, Winterthur / Switzerland 1.12 Effect of gravitational force and compensation with inclination measuring instruments The inclination displayed by inclination measuring instruments and sensors is based on the gravitation. However, gravitational force is not consistent around the globe, varying with latitude and height above sea level. Furthermore, variations of the density in the lithosphere cause additional local deviations. As an example, the gravity at sea level is • 9.78033 m/s2 at the equator • 9.80620 m/s2 at 45 degree of latitude • 9.83219 m/s2...

Compendium inclination measurement WYLER AG, Winterthur / Switzerland 1.13 Measuring uncertainty In order to perform a valid measurement, a number of conditions must be fulfilled. A precision measurement is usually dependent on the influence of a number of different factors, such as: • Temperature of the object and ambient temperature • Temperature of the measuring instrument • Linearity of the measuring instrument • Vibrations • Dirt, dust, and humidity These influencing factors are generally termed measuring uncertainty. What are the major causes of measuring uncertainty? Measurements can never...