Ground Sample Distance (GSD)

Ground sample distance is the most quoted number in drone mapping and the most misunderstood. The geometry is nothing but similar triangles: a pixel of width $p$ sits at distance $f$ behind the lens, the ground sits at distance $H$ in front of it, and the two triangles that share the lens as their apex give $\mathrm{GSD}/H = p/f$ directly. Rearranged, $\mathrm{GSD} = Hp/f$. That is the whole derivation, and it has not changed since the first camera was pointed out of a balloon.

Now the part that matters. GSD is not resolution. It is the ground spacing of the pixel CENTRES — a sampling interval, nothing more. Whether a feature that size can actually be seen depends on what the optical system delivers to those pixels, and every stage of it costs you. The lens has a modulation transfer function that softens fine detail before it reaches the sensor. The Bayer colour filter array means each photosite samples only one colour and the rest is interpolated. Residual forward motion smears the image while the shutter is open. Haze scatters light into the shadows and lowers contrast. Between them these routinely cost a factor of two to three, so a 2 cm GSD gives you features that read at nearer 4 to 6 cm. Sampling theory says as much on its own: you need at least two samples across a feature before it is even representable, and a feature you can confidently identify usually wants four or five.

And GSD is emphatically not accuracy. This is the claim that costs people money. The horizontal accuracy of a mapping deliverable is set by how well the block is tied to the ground — by the number, distribution and quality of the ground control points, by how well the camera's interior orientation was recovered, and by how the bundle adjustment converged. Pixel size is one small term inside all that. A block flown at 1.5 cm GSD with no ground control and a bare consumer GNSS inherits that receiver's error, which is metres, and no amount of resolution rescues it. The same block with well-distributed checked control and a good adjustment might reach two or three centimetres horizontally — better than most jobs need, and still not 1.5 cm. When a proposal says "1.5 cm accuracy" because the flight planner printed "1.5 cm GSD", that is not a specification, it is a category error, and it is the single commonest overstatement in the industry.

The vertical case is worse again, and has its own page here. Height comes out of the intersection of rays from different exposures, and how well that intersection is conditioned depends on the base-to-height ratio, which on a typical high-overlap drone flight is about 0.1. Vertical precision runs eight or ten times the GSD as a matter of routine geometry. If somebody quotes you the same number for horizontal and vertical accuracy, they have not done the calculation.

The arithmetic traps. Focal length is in millimetres and pixel pitch is in micrometres, a thousand-fold apart, and mixing them without converting gives an answer off by exactly a thousand — which is at least obvious. The subtle one is the 35 mm EQUIVALENT focal length. Camera makers quote it because it means something to photographers, and it is not the focal length in this equation. A one-inch sensor with a true 8.8 mm lens is marketed as "24 mm equivalent"; use 24 and your GSD comes out nearly three times too small. Read the EXIF FocalLength field, not FocalLengthIn35mmFormat.

The other trap is the height datum. $H$ is the distance from the camera to THE GROUND BEING IMAGED. A drone that reports 100 m relative to its take-off point is only 60 m above a hill that rises 40 m, and over that hill the GSD is 40% finer than planned — while over a valley 40 m below take-off it is 40% coarser. On rolling terrain a single-altitude flight simply does not have one GSD, and terrain-following, or splitting the site into blocks by elevation, is the only honest fix. This is the same effect that makes a raw aerial photograph have no single scale, and it is the reason orthorectification exists.

Finally, a word on what a finer GSD costs, because it is not linear. Halving the GSD means halving the flying height, which halves both footprint dimensions, which halves both the air base and the line spacing — so the image count goes up FOURFOLD, and so does roughly everything downstream: flight time, battery swaps, storage, matching time, and the size of the model you have to hand over. Choose the GSD from what the client genuinely needs to identify, not from what looks impressive on a cover page.