Drone volume surveys: method, accuracy and deliverables

The principle: a volume between two surfaces

A volume survey calculates the volume contained between two surfaces: the measured surface (the top of the stockpile or the ground) and a reference surface (its base, the original ground, an earlier survey or the design). The drone does not measure volume directly: it produces a very dense digital surface model (DSM), and the volume is then calculated as the difference with the reference.

The software divides the area into cells a few centimetres wide. For each cell it multiplies the cell area by the height difference between the two surfaces, then adds everything up. Cells above the reference give the fill (or the stockpile); cells below give the cut.

How a survey runs

1. Flight plan. The drone flies parallel lines with a high overlap between photos. For the general case, Pix4D recommends at least 75 % overlap along the flight direction and 60 % between lines, and more on low-texture or vegetated surfaces.
2. Ground control. Ground control points (GCPs) measured with GNSS RTK, and/or an RTK-equipped drone, place the model in the site’s coordinate system, horizontally and vertically.
3. Photogrammetry. The software matches the same details across several photos, computes the position of each image, then builds a dense point cloud and the DSM.
4. Boundaries. The outline of each stockpile or zone is drawn on the orthophoto, along the toe of the pile.
5. Calculation and checks. Volumes are calculated zone by zone, then checked: errors on check points, model consistency, comparison with the previous survey.

Choosing the reference surface

This choice often has more influence on the result than the accuracy of the drone itself. Photogrammetry software offers several base surfaces, each suited to a situation:

• Triangulated base along the outline: the base connects the points along the toe of the pile. The usual case for a stockpile on open ground whose whole perimeter is visible.
• Fitted plane: a horizontal or inclined plane is fitted to the outline. Useful for a stockpile on an evenly sloping platform.
• Horizontal plane at a set level: at the lowest point of the outline or at a known elevation. Preferred when part of the toe is hidden, for example a stockpile against a wall or in a bay.
• Earlier survey: two surveys are compared (month M and M-1, before and after works) to see what was added or removed.
• Design surface: in earthworks, the as-built ground is compared with the engineer’s design to find the remaining cut and fill.

The base is agreed with the operator or the project engineer, described in the report and kept from one survey to the next: that is what makes the figures comparable over time.

What accuracy to expect

Accuracy depends on the ground sampling distance (GSD), the quality of the ground control, the texture of the materials, flight conditions and, above all, how the base is defined.

The GSD is calculated from the camera and the flight height:

GSD = (sensor width × flight height) / (focal length × image width in pixels)

For the DJI Mavic 3 Enterprise, DJI gives GSD ≈ H/36.5 (GSD in cm, H in metres), about 2.7 cm per pixel at a height of 100 m. Pix4D states that a correctly reconstructed and georeferenced project generally reaches 1 to 2 times the GSD horizontally and 1 to 3 times the GSD vertically.

A simple calculation shows why elevation matters so much: a 2 cm bias over the whole footprint of a 5,000 m² stockpile amounts to 100 m³. Hence the importance of vertical control and check points.

Published comparisons on well-defined stockpiles report differences of around one percent, sometimes less, between drone volumes and GNSS or laser-scanner surveys. Conversely, a poorly defined stockpile or one sitting on uneven ground can produce a much larger error whatever the method, which is why the base is agreed and documented with you.

From volume to tonnage

The drone measures cubic metres as they sit in the pile. To obtain tonnes you need the material’s bulk density (t/m³), which depends on the product, its grading, its moisture and its compaction. The value is supplied by the operator or measured on site (by weighing a known volume) and appears in the report, because any density error carries straight into the tonnage.

How often to measure

For an inventory, frequency follows reporting: monthly, quarterly or at each period close. On an earthworks site, surveys are usually tied to key stages: baseline, end of topsoil stripping, end of cut, handover of platforms.

A saved flight plan, permanent control points and a similar time slot from one survey to the next keep measurements comparable, which makes period-to-period differences more reliable.

Deliverables

• Volume table by stockpile, zone or date, with differences between surveys (Excel, PDF).
• Annotated orthophoto showing the outline and volume of each stockpile.
• 3D model or DSM of the area, to view and check the calculation boundaries.
• Report: coordinate system, reference surfaces, densities used, checks and results.

Preparing the survey: a checklist

• Access, site safety rules and an on-site contact.
• List and location of the stockpiles or zones to measure.
• Material types and densities, if you need tonnages.
• Preferred reference surface: base, earlier survey or design.
• Site coordinate system and any known survey points.
• Survey frequency and reporting dates.

Sources

1. DJI Enterprise, Geospatial Solutions FAQ (Mavic 3E GSD)
2. Pix4D, image acquisition plan and overlap
3. Pix4D, relative and absolute accuracy of drone mapping
4. Pix4D, choosing the base surface for a volume calculation
5. Raeva, Filipova and Filipov (2016), stockpile volume by GPS and UAV in an open-pit quarry, ISPRS Archives

Manufacturer figures and published orders of magnitude: the accuracy of a given project is demonstrated on its own check points.

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