Pocket rockets are some of the most difficult and frustrating BIF subjects. I have been trying for 20 years, and it is not easy and success rate is low. Best is to try and get them when they leave the perch, but they are so fast and unpredictable, that your do not know which way they are going to go off to. So, pre-focus on the subject them realign so that there is space for the bird to fly into the frame. Now you must anticipate when the subject will fly in or off, and you start shooting before that happens. I append an image where this was done.
Since autofocus works on contrast difference, if the subject is the size of the focus point or slightly larger, the camera often has no clue what you are trying to lock focus on so the result is often blurred images. Panning against clear, blue skies is different. Once the auto focus catches on, you can normally get plenty of keepers. I use the D850 and D500, but it was the same for the D4, D3S, D600, D800; D750 etc.
Shooting KF's or bee-eaters diving into or out of the water or swallows sipping off the water surface is the same problem, if the focus does not lock, no luck.
However, the harder you try, the luckier you get
Village Weaver, but the BG was OK so picking up was easier. D500; 500 PF@ F/7.1; 1/1600; ISO 500
The SS is way too slow for frozen wings, but I do not necessarily want frozen wings all the time; for frozen wings, then I go for >1/4000/s
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