File Exchange > Graphing >    Abbott-Firestone Curve

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Create Abbott-Firestone curve and calculate Rk family values.

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This app can be used to create Abbott-Firestone curve and calculate Rk, Rpk and Rvk values. Abbott-Firestone curve is also called Bearing Area curve (BAC) or Material Ratio curve.
Download the file Abbott-Firestone_Curve.opx, and then drag-and-drop onto the Origin workspace. An icon will appear in the Apps Gallery window.
NOTE: This tool requires OriginPro.

  1. Make a worksheet active. Click Abbott-Firestone Curve app icon in Apps Gallery window.
  2. In the opened dialog, select XY data for roughness input data.
  3. Click OK button. A graph with a Abbott-Firestone curve and a table for Rk family values will be created.

This app provides a sample OPJU file. Right click on the Abbott-Firestone Curve icon in the Apps Gallery window, and choose Show Samples Folder from the short-cut menu. A folder will open. Drag-and-drop the project file BACEx.opju from the folder onto Origin. The Notes1 window in the project shows detailed steps.
Note: If you wish to save the OPJU after changing, it is recommended that you save to a different folder location (e.g. User Files Folder).


  1. Calculate the empirical cumulative distribution function for the roughness data, and create the bearing area curve.
  2. Find the 40% segment of the curve which is the flattest and has the smallest absolute slope.
  3. Fit the 40% segment with a linear function, extend the line to x=0% and 100% and denote two end points with P1 and P2. Draw two horizontal lines from P1 and P2 respectively, and intersect with the bearing area curve at P3 and P4.
  4. Draw two straight lines from P3 and P4 respectively, intersect with the vertical axes for 0% and 100% at P5 and P6, so that the area of the triangle P1P3P5 equals to the area between the horizontal line P1P3 and the the bearing area curve, and the same rule for the triangle P2P4P6.
  5. Core Roughness DepthRk, is the vertical distance between two horizontal lines P1P3 and P2P4.
    Reduced Peak HeightRpk, is the height (P1P5) of the upper left triangle.
    Reduced Valley DepthRvk, is the height (P6P2) of the lower right triangle.
    Material Ratio 1Mr1, is the x value of P3.
    Material Ratio 2Mr2, is the x value of P4.

Related Apps

  1. Surface Roughness Parameters


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