Sand topdressing by exact depth: how to work it out

Today I explained the same calculation about sand topdressing for the third time, so I need to write a blog post on this topic.

This is following the method of David Robinson, who says when you’ve written the same code 3 times, write a function; when you’ve given the same advice 3 times, write a blog post; and when you’ve done the blog post 3 times, write a book.

The best way to express sand topdressing amount, standardized so it makes sense to anyone in the world, is as a depth. I’ve generally figured that out by taking the volume of sand applied, divided by the area to which it was applied, and making a correction for overthrow.

The USGA has produced this video showing an exact way to measure sand topdressing application rate, with no need for the overthrow correction, and this measures in mass.

You could, of course, figure out the volume by looking at the volume displacement when the sand is added to a known amount of water. But we can also assume that the sand has a bulk density (when dry) of about 1.5 g/cm³. I generally use 1.5. That’s a common conversion factor for sand-based rootzones used in turfgrass. In civil engineering I think sand is often assumed to have a bulk density of 1.63 g/cm³. Whether you use 1.5 or 1.63 or something close to either of those, we are going to be within about 10% of the real number.

If one measures the mass of sand applied to a known area, the depth calculation is simple. I do this in metric units, because I want to express the depth in mm, which is going to give a number between 0 and about 35; I’ve never met a turfgrass manager who applies more than 35 mm of sand per year (about 115 ft³/1000 ft²).

You have a collection container of known dimensions. Let’s say it happens to be 2,000 cm², and in that container you’ve collected 400 g of sand.

To express that in mm, we want to convert the mass to a volume, and then divide by the area. Volume divided by area gives depth. I’m going to work with a bulk density of 1.5.

$ 10(\frac{\frac{400}{1.5}}{2000}) = $ sand depth of 1.3 mm

Take the mass in grams, divide by the bulk density and the area to which the sand was applied in cm², and multiply by ten. That gives the depth in mm. You can adjust the equation as necessary if you wish to use other units.