How Do I Calculate Scallop Height & Surface Finish?

Scallop height and surface finish are two measurements that are used for characterizing surfaces, particularly when the surface is created using a cutting tool.

Scallop Height

The scallop tool creates a constant scallop across a surface. A scallop resembles a small round indentation. When several scallops are created in a row the peaks and valleys occur in the surface. The surface finish directly relates to the roughness of the surface. There are several different methods to calculate the surface roughness. Most will use a computer or digital device that takes the minute measurement and produces the roughness from a correlation chart.

Determine the radius (r) of the cutting tool. This is equivalent to one half of the diameter of the cutting tool. Check the tool specifications to see if the radius is noted. If not, use a measuring tape with small gradations and measure the diameter to calculate the radius. If the diameter is 8 inches then the radius would be 4 inches.

Calculate the tool path spacing (c). This is the second measurement needed to calculate the scallop height. The tool path spacing is also known as the step over. This is the distance from one end of the scallop measured straight to the other end of the scallop. Many times this measurement is taken from the middle of one scallop to the middle of an adjacent scallop.

Square the radius by taking the radius measurement and multiplying it by itself. Multiply the radius squared by four (4r^2). Subtract from this number the tool path spacing squared (c^2). Take the square root of this number and multiply the answer by one half. Subtract this number from the radius measurement. The resulting number is the scallop height. The full equation is as follows: scallop height = r - 0.5square root (4r^2 - c^2)

Surface Finish

Measure the surface roughness with a stylus device. There is a probe on the tip of the stylus. The probe moves along the surface of the material and traces any irregularities. The vertical and perpendicular movement is recorded by the stylus. From the movement of the probe it is possible to calculate the surface finish. The probe feeds the information to a computer that produces the surface finishing rating. Investigate the type of material used on the stylus, as some material, such as diamonds, can produce scratches.

Compare the surface finish to another surface that was made with the same material, process and parameters. Run your fingers over the two surfaces to determine if one is rougher than the other. Carefully look at the surface to see if there are any visual differences. It is best to compare the surface finishing to a surface finishing tablet that contains different finishing standards. Choose the standard that the surface closest resembles. This method is highly subjective and depends on the person inspecting the surface.

Analyze the surface finish as the surface is being created. This requires some specialized equipment and computers but you will be able to notice problems immediately which can greatly reduce an inferior or low-quality product. A common machine to measure surface finish uses a light or camera that scans the surface. The digital image is then fed into a computer that will compare the surface image into numerical data. This numerical data is compared to correlation charts that provide a surface finishing rating.

Things You Will Need

  • Measuring tape
  • Stylus device
  • Light

About the Author

Liz Tomas began writing professionally in 2004. Her work has appeared in the "American Journal of Enology and Viticulture," "BMC Genomics" and "PLoS Biology." She holds a Master of Science in food science from Cornell University and a Bachelor of Science in biochemistry from the University of New Hampshire. She is pursuing her Ph.D. in oenology at Lincoln University.