Vertical ShapeArray data is most commonly expressed as cumulative deviation (Absolute Shape) data. Each reading from the ShapeArray is expressed as a set of Cartesian X, Y, and Z coordinates for each segment of the instrument that are combined to model the shape of the instrument in three dimensions. The orientation of the axes in ShapeArray data correspond to a physical marking on the instrument known as the X-Mark. Vertical ShapeArray data axes are oriented in the following manner:

  • Positive X (+X) axis is in the direction of the X-Mark
  • Positive Y (+Y) axis is 90 degrees counterclockwise from the +X axis
  • Positive Z (+Z) axis is up relative to gravity

The only connection between ShapeArray data and the real world is the X-Mark on the instrument. To orient the data collected from a ShapeArray to the real world, an azimuth offset angle must be measured from a known direction to the physical X-Mark on the instrument.

For example, a marker on site or magnetic North as measured by a compass can be used as the reference direction for measuring the offset angle. The measured azimuth offset angle is then input into Measurand’s software to automatically re-orient the ShapeArray data so that the axes align with the desired real world direction.


The SAA X-Mark Protractor article on our Support web site describes how to use the included SAA X-Mark Protractor to measure an azimuth offset angle during ShapeArray installation.


For example, the figure below shows a top-down view of an inclinometer casing whose A+ groove is oriented 45 degrees counterclockwise from magnetic North (i.e. A+ is to the North-West). A ShapeArray has been installed in this casing with the physical X-mark towards the West.


Figure 1: A top down view of an example ShapeArray installed in inclinometer casing


The following observations about this example installation can be made:

  • In ShapeArray data, the Y axis is a mirror of inclinometer data’s B axis. In other words, when the ShapeArray data is perfectly aligned with the inclinometer data, the +Y axis will be equivalent to the -B axis.
  • When measuring the azimuth offset angle, the measurement is always performed from the reference direction to the ShapeArray’s X-Mark in a clockwise direction. This implies the following:
    • To orient the ShapeArray’s +X axis to magnetic North, an azimuth offset of 270 degrees must be applied in the software.
    • To orient the ShapeArray’s +X axis to inclinometer casing’s A+ groove, an azimuth offset of 315 degrees must be applied in the software.