Motion Blur Speed Limit

While the shutter is open, the aircraft moves and the image moves with it. The ground distance covered during the exposure is $V_g t_{exp}$, and that smear lands on the sensor as a blur measured in pixels: $V_g t_{exp}/\mathrm{GSD}$. Set that equal to whatever fraction of a pixel you are willing to accept, rearrange, and you have the fastest ground speed the plan allows.

This is the honest limit on resolution and it is almost never checked. A mission planner will happily accept a 1.5 cm GSD at 12 m/s, and in flat overcast light the camera falls back to 1/250 s to hold its exposure. That is 4.8 cm of smear — more than three pixels — and the map that comes out is a 5 cm product wearing a 1.5 cm label. Nothing in the workflow flags it. The GSD calculation is still arithmetically correct; it simply describes a sampling interval that the optics are no longer delivering detail into.

Half a pixel is the usual budget and it is a convention rather than a threshold. Blur degrades the modulation transfer function continuously — there is no step where the image suddenly becomes bad — and half a pixel is simply a level at which the smear contributes less than the other softening effects already present. Some specifications work to a third of a pixel, some tolerate a whole one. What matters is that a number is chosen and checked, rather than left implicit.

There are only three levers, and it is worth knowing what each costs. Shorten the exposure: this costs light, which means opening the aperture (with a loss of depth of field and usually of corner sharpness) or raising ISO (with noise that itself degrades matching). Slow the aircraft: this costs flight time and battery, and is the one that always works. Accept a coarser GSD: this costs nothing but honesty, and is frequently the right answer. What is NOT a lever is buying a finer GSD — look at the equation and notice that halving the GSD halves the allowed speed. Chasing resolution without slowing down loses on both sides at once.

Two effects the equation cannot see. The first is angular motion. It counts forward translation only, so a multirotor rocking in gusts or a fixed wing banking through a turn adds smear from rotation that this ignores entirely — which is a good reason to discard images taken during turns rather than feed them to the adjustment. The second, and larger, is rolling shutter. A rolling-shutter sensor exposes the image line by line over several milliseconds, so a moving aircraft records a frame that is geometrically SHEARED rather than merely blurred. That is a distortion, not a softness: no exposure time removes it, it biases the bundle adjustment systematically rather than randomly, and it is a well-known contributor to the bowl-shaped deformation that uncontrolled drone blocks develop. A global shutter or a mechanical leaf shutter has no such effect, and that difference is a large part of why a mapping payload costs more than a camera with the same sensor in it.

Run the equation the other way and it becomes a diagnostic. Take the ground speed from the flight log and the exposure time from the EXIF of an image you already flew, and it tells you how many pixels of smear that flight actually carried. It is a five-minute check and it settles a lot of arguments about why a deliverable looks softer than the specification promised.