# Basics

### 1. What is an "INCLINATION"?

The definition ANGLE is the difference between two straight lines g1 and g2 ina flat plane. A angle will be created at the cross section between the two lines g1 and g2.

The inclination is a specific angle related to the angle a created between the line g3 and a horizontal line g4, whereas the horizontal line g4 lies in the intersection between a vertical plane E2 and the horizontal (reference) plane E1, which must be absolutely horizontal.

With an inclination measuring instrument not only an angle can be detected but also, related on the base length, the heights of a point (topography of a surface) may be defined. This fact and the simple use of an electronic inclination measuring instrument allows the efficient measuring of machine tool guide ways and surfaces.

# 2. What is a positive, respectively negative inclination?

A positive inclination is, when the line respectively the plane,in the measuring direction is inclined. The negative inclination istherefore when the line or plane is declined

# 3. Reversal measurement

Thanks to the reversal measurement, it is possible to make precise absolute measurements (measuring the precise absolute deviation from center of gravity) even by using inclinometers with zero deviation. As shown in the following example it is possible to define:

I. the zero point deviation of the instrument itself

II. the exact inclination of the object to be measured in relation to the absolute center of gravity

The measuring instrument has to be placed on a clean horizontally adjusted surface in a defined and marked spot. The measured value is the value „A“. The instrument has then to be turned by 180° and placed again exactly at the same spot. The second value is value “B”.

# 4. Units used for inclination measurement

Depending on the size of the angle different units are used. Roughly speaking two basic groups ca be defined: small and large inclinations.

## For large inclinations | |

xx°xx’xx’’ | Deg / Arcmin / Arcsec |

xx,xx DEG | Degree with two digits |

x,xx Rad | Radiant |

x,xx mRad | Milliradiant |

x,xx % | Percent |

xx,xx’’/10’’ | Inch / 10 inch |

xx,xx’’/12’’ | Inch / 12 inch |

gon | New degree |

## For small inclinations | |

xx°xx’xx’’ | Deg / Arcmin / Arcsec |

xx,xx DEG | Degree with two digits |

x,xx mRad | Milliradiant |

x,xx µRad | Microradiant |

x,xxx mm/m | Height in [mm] related to base length of 1 m |

x,x µm/m | Height in [µm] related to base length of 1 m |

x,x mm/0.5 m | Height in [mm] related to relative base length of 0,5 m |

xx,xx’’/10’’ | Inch / 10 inch |

xx,xx’’/12’’ | Inch / 12 inch |

# 6. What does "1 µm/m" means?

It is quite difficult to imagine an angle of the size of 1µm/m. Using a small mathematical treat it becomes more imaginable. By multiplying the length “L” and the height “h” by factor 1000 the relation remains the same.

For comparison: A human hair has a diameter of approximately 50 up to 75µm!